[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[40] | 2 | * |
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[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[40] | 4 | * |
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[440] | 5 | * Copyright (C) 2003-2009 |
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[40] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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[406] | 19 | namespace lemon { |
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| 20 | |
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[40] | 21 | /** |
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| 22 | @defgroup datas Data Structures |
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[550] | 23 | This group contains the several data structures implemented in LEMON. |
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[40] | 24 | */ |
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| 25 | |
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| 26 | /** |
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| 27 | @defgroup graphs Graph Structures |
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| 28 | @ingroup datas |
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| 29 | \brief Graph structures implemented in LEMON. |
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| 30 | |
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[209] | 31 | The implementation of combinatorial algorithms heavily relies on |
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| 32 | efficient graph implementations. LEMON offers data structures which are |
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| 33 | planned to be easily used in an experimental phase of implementation studies, |
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| 34 | and thereafter the program code can be made efficient by small modifications. |
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[40] | 35 | |
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| 36 | The most efficient implementation of diverse applications require the |
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| 37 | usage of different physical graph implementations. These differences |
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| 38 | appear in the size of graph we require to handle, memory or time usage |
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| 39 | limitations or in the set of operations through which the graph can be |
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| 40 | accessed. LEMON provides several physical graph structures to meet |
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| 41 | the diverging requirements of the possible users. In order to save on |
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| 42 | running time or on memory usage, some structures may fail to provide |
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[83] | 43 | some graph features like arc/edge or node deletion. |
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[40] | 44 | |
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[209] | 45 | Alteration of standard containers need a very limited number of |
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| 46 | operations, these together satisfy the everyday requirements. |
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| 47 | In the case of graph structures, different operations are needed which do |
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| 48 | not alter the physical graph, but gives another view. If some nodes or |
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[83] | 49 | arcs have to be hidden or the reverse oriented graph have to be used, then |
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[209] | 50 | this is the case. It also may happen that in a flow implementation |
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| 51 | the residual graph can be accessed by another algorithm, or a node-set |
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| 52 | is to be shrunk for another algorithm. |
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| 53 | LEMON also provides a variety of graphs for these requirements called |
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| 54 | \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only |
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| 55 | in conjunction with other graph representations. |
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[40] | 56 | |
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| 57 | You are free to use the graph structure that fit your requirements |
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| 58 | the best, most graph algorithms and auxiliary data structures can be used |
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[314] | 59 | with any graph structure. |
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| 60 | |
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| 61 | <b>See also:</b> \ref graph_concepts "Graph Structure Concepts". |
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[40] | 62 | */ |
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| 63 | |
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| 64 | /** |
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[451] | 65 | @defgroup graph_adaptors Adaptor Classes for Graphs |
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[416] | 66 | @ingroup graphs |
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[451] | 67 | \brief Adaptor classes for digraphs and graphs |
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| 68 | |
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| 69 | This group contains several useful adaptor classes for digraphs and graphs. |
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[416] | 70 | |
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| 71 | The main parts of LEMON are the different graph structures, generic |
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[451] | 72 | graph algorithms, graph concepts, which couple them, and graph |
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[416] | 73 | adaptors. While the previous notions are more or less clear, the |
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| 74 | latter one needs further explanation. Graph adaptors are graph classes |
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| 75 | which serve for considering graph structures in different ways. |
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| 76 | |
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| 77 | A short example makes this much clearer. Suppose that we have an |
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[451] | 78 | instance \c g of a directed graph type, say ListDigraph and an algorithm |
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[416] | 79 | \code |
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| 80 | template <typename Digraph> |
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| 81 | int algorithm(const Digraph&); |
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| 82 | \endcode |
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| 83 | is needed to run on the reverse oriented graph. It may be expensive |
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| 84 | (in time or in memory usage) to copy \c g with the reversed |
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| 85 | arcs. In this case, an adaptor class is used, which (according |
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[451] | 86 | to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph. |
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| 87 | The adaptor uses the original digraph structure and digraph operations when |
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| 88 | methods of the reversed oriented graph are called. This means that the adaptor |
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| 89 | have minor memory usage, and do not perform sophisticated algorithmic |
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[416] | 90 | actions. The purpose of it is to give a tool for the cases when a |
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| 91 | graph have to be used in a specific alteration. If this alteration is |
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[451] | 92 | obtained by a usual construction like filtering the node or the arc set or |
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[416] | 93 | considering a new orientation, then an adaptor is worthwhile to use. |
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| 94 | To come back to the reverse oriented graph, in this situation |
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| 95 | \code |
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| 96 | template<typename Digraph> class ReverseDigraph; |
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| 97 | \endcode |
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| 98 | template class can be used. The code looks as follows |
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| 99 | \code |
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| 100 | ListDigraph g; |
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[451] | 101 | ReverseDigraph<ListDigraph> rg(g); |
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[416] | 102 | int result = algorithm(rg); |
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| 103 | \endcode |
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[451] | 104 | During running the algorithm, the original digraph \c g is untouched. |
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| 105 | This techniques give rise to an elegant code, and based on stable |
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[416] | 106 | graph adaptors, complex algorithms can be implemented easily. |
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| 107 | |
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[451] | 108 | In flow, circulation and matching problems, the residual |
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[416] | 109 | graph is of particular importance. Combining an adaptor implementing |
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[451] | 110 | this with shortest path algorithms or minimum mean cycle algorithms, |
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[416] | 111 | a range of weighted and cardinality optimization algorithms can be |
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| 112 | obtained. For other examples, the interested user is referred to the |
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| 113 | detailed documentation of particular adaptors. |
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| 114 | |
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| 115 | The behavior of graph adaptors can be very different. Some of them keep |
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| 116 | capabilities of the original graph while in other cases this would be |
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[451] | 117 | meaningless. This means that the concepts that they meet depend |
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| 118 | on the graph adaptor, and the wrapped graph. |
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| 119 | For example, if an arc of a reversed digraph is deleted, this is carried |
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| 120 | out by deleting the corresponding arc of the original digraph, thus the |
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| 121 | adaptor modifies the original digraph. |
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| 122 | However in case of a residual digraph, this operation has no sense. |
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[416] | 123 | |
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| 124 | Let us stand one more example here to simplify your work. |
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[451] | 125 | ReverseDigraph has constructor |
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[416] | 126 | \code |
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| 127 | ReverseDigraph(Digraph& digraph); |
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| 128 | \endcode |
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[451] | 129 | This means that in a situation, when a <tt>const %ListDigraph&</tt> |
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[416] | 130 | reference to a graph is given, then it have to be instantiated with |
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[451] | 131 | <tt>Digraph=const %ListDigraph</tt>. |
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[416] | 132 | \code |
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| 133 | int algorithm1(const ListDigraph& g) { |
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[451] | 134 | ReverseDigraph<const ListDigraph> rg(g); |
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[416] | 135 | return algorithm2(rg); |
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| 136 | } |
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| 137 | \endcode |
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| 138 | */ |
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| 139 | |
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| 140 | /** |
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[50] | 141 | @defgroup semi_adaptors Semi-Adaptor Classes for Graphs |
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[40] | 142 | @ingroup graphs |
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| 143 | \brief Graph types between real graphs and graph adaptors. |
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| 144 | |
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[550] | 145 | This group contains some graph types between real graphs and graph adaptors. |
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[209] | 146 | These classes wrap graphs to give new functionality as the adaptors do it. |
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[50] | 147 | On the other hand they are not light-weight structures as the adaptors. |
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[40] | 148 | */ |
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| 149 | |
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| 150 | /** |
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[209] | 151 | @defgroup maps Maps |
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[40] | 152 | @ingroup datas |
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[50] | 153 | \brief Map structures implemented in LEMON. |
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[40] | 154 | |
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[550] | 155 | This group contains the map structures implemented in LEMON. |
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[50] | 156 | |
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[314] | 157 | LEMON provides several special purpose maps and map adaptors that e.g. combine |
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[40] | 158 | new maps from existing ones. |
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[314] | 159 | |
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| 160 | <b>See also:</b> \ref map_concepts "Map Concepts". |
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[40] | 161 | */ |
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| 162 | |
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| 163 | /** |
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[209] | 164 | @defgroup graph_maps Graph Maps |
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[40] | 165 | @ingroup maps |
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[83] | 166 | \brief Special graph-related maps. |
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[40] | 167 | |
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[550] | 168 | This group contains maps that are specifically designed to assign |
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[406] | 169 | values to the nodes and arcs/edges of graphs. |
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| 170 | |
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| 171 | If you are looking for the standard graph maps (\c NodeMap, \c ArcMap, |
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| 172 | \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts". |
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[40] | 173 | */ |
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| 174 | |
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| 175 | /** |
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| 176 | \defgroup map_adaptors Map Adaptors |
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| 177 | \ingroup maps |
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| 178 | \brief Tools to create new maps from existing ones |
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| 179 | |
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[550] | 180 | This group contains map adaptors that are used to create "implicit" |
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[50] | 181 | maps from other maps. |
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[40] | 182 | |
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[406] | 183 | Most of them are \ref concepts::ReadMap "read-only maps". |
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[83] | 184 | They can make arithmetic and logical operations between one or two maps |
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| 185 | (negation, shifting, addition, multiplication, logical 'and', 'or', |
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| 186 | 'not' etc.) or e.g. convert a map to another one of different Value type. |
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[40] | 187 | |
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[50] | 188 | The typical usage of this classes is passing implicit maps to |
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[40] | 189 | algorithms. If a function type algorithm is called then the function |
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| 190 | type map adaptors can be used comfortable. For example let's see the |
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[314] | 191 | usage of map adaptors with the \c graphToEps() function. |
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[40] | 192 | \code |
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| 193 | Color nodeColor(int deg) { |
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| 194 | if (deg >= 2) { |
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| 195 | return Color(0.5, 0.0, 0.5); |
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| 196 | } else if (deg == 1) { |
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| 197 | return Color(1.0, 0.5, 1.0); |
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| 198 | } else { |
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| 199 | return Color(0.0, 0.0, 0.0); |
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| 200 | } |
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| 201 | } |
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[209] | 202 | |
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[83] | 203 | Digraph::NodeMap<int> degree_map(graph); |
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[209] | 204 | |
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[314] | 205 | graphToEps(graph, "graph.eps") |
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[40] | 206 | .coords(coords).scaleToA4().undirected() |
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[83] | 207 | .nodeColors(composeMap(functorToMap(nodeColor), degree_map)) |
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[40] | 208 | .run(); |
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[209] | 209 | \endcode |
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[83] | 210 | The \c functorToMap() function makes an \c int to \c Color map from the |
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[314] | 211 | \c nodeColor() function. The \c composeMap() compose the \c degree_map |
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[83] | 212 | and the previously created map. The composed map is a proper function to |
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| 213 | get the color of each node. |
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[40] | 214 | |
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| 215 | The usage with class type algorithms is little bit harder. In this |
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| 216 | case the function type map adaptors can not be used, because the |
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[50] | 217 | function map adaptors give back temporary objects. |
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[40] | 218 | \code |
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[83] | 219 | Digraph graph; |
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| 220 | |
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| 221 | typedef Digraph::ArcMap<double> DoubleArcMap; |
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| 222 | DoubleArcMap length(graph); |
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| 223 | DoubleArcMap speed(graph); |
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| 224 | |
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| 225 | typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap; |
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[40] | 226 | TimeMap time(length, speed); |
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[209] | 227 | |
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[83] | 228 | Dijkstra<Digraph, TimeMap> dijkstra(graph, time); |
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[40] | 229 | dijkstra.run(source, target); |
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| 230 | \endcode |
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[83] | 231 | We have a length map and a maximum speed map on the arcs of a digraph. |
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| 232 | The minimum time to pass the arc can be calculated as the division of |
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| 233 | the two maps which can be done implicitly with the \c DivMap template |
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[40] | 234 | class. We use the implicit minimum time map as the length map of the |
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| 235 | \c Dijkstra algorithm. |
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| 236 | */ |
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| 237 | |
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| 238 | /** |
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[209] | 239 | @defgroup matrices Matrices |
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[40] | 240 | @ingroup datas |
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[50] | 241 | \brief Two dimensional data storages implemented in LEMON. |
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[40] | 242 | |
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[550] | 243 | This group contains two dimensional data storages implemented in LEMON. |
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[40] | 244 | */ |
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| 245 | |
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| 246 | /** |
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| 247 | @defgroup paths Path Structures |
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| 248 | @ingroup datas |
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[318] | 249 | \brief %Path structures implemented in LEMON. |
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[40] | 250 | |
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[550] | 251 | This group contains the path structures implemented in LEMON. |
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[40] | 252 | |
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[50] | 253 | LEMON provides flexible data structures to work with paths. |
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| 254 | All of them have similar interfaces and they can be copied easily with |
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| 255 | assignment operators and copy constructors. This makes it easy and |
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[40] | 256 | efficient to have e.g. the Dijkstra algorithm to store its result in |
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| 257 | any kind of path structure. |
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| 258 | |
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| 259 | \sa lemon::concepts::Path |
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| 260 | */ |
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| 261 | |
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| 262 | /** |
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| 263 | @defgroup auxdat Auxiliary Data Structures |
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| 264 | @ingroup datas |
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[50] | 265 | \brief Auxiliary data structures implemented in LEMON. |
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[40] | 266 | |
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[550] | 267 | This group contains some data structures implemented in LEMON in |
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[40] | 268 | order to make it easier to implement combinatorial algorithms. |
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| 269 | */ |
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| 270 | |
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| 271 | /** |
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| 272 | @defgroup algs Algorithms |
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[550] | 273 | \brief This group contains the several algorithms |
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[40] | 274 | implemented in LEMON. |
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| 275 | |
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[550] | 276 | This group contains the several algorithms |
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[40] | 277 | implemented in LEMON. |
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| 278 | */ |
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| 279 | |
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| 280 | /** |
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| 281 | @defgroup search Graph Search |
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| 282 | @ingroup algs |
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[50] | 283 | \brief Common graph search algorithms. |
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[40] | 284 | |
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[550] | 285 | This group contains the common graph search algorithms, namely |
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[406] | 286 | \e breadth-first \e search (BFS) and \e depth-first \e search (DFS). |
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[40] | 287 | */ |
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| 288 | |
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| 289 | /** |
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[314] | 290 | @defgroup shortest_path Shortest Path Algorithms |
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[40] | 291 | @ingroup algs |
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[50] | 292 | \brief Algorithms for finding shortest paths. |
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[40] | 293 | |
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[550] | 294 | This group contains the algorithms for finding shortest paths in digraphs. |
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[406] | 295 | |
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| 296 | - \ref Dijkstra algorithm for finding shortest paths from a source node |
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| 297 | when all arc lengths are non-negative. |
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| 298 | - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths |
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| 299 | from a source node when arc lenghts can be either positive or negative, |
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| 300 | but the digraph should not contain directed cycles with negative total |
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| 301 | length. |
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| 302 | - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms |
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| 303 | for solving the \e all-pairs \e shortest \e paths \e problem when arc |
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| 304 | lenghts can be either positive or negative, but the digraph should |
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| 305 | not contain directed cycles with negative total length. |
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| 306 | - \ref Suurballe A successive shortest path algorithm for finding |
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| 307 | arc-disjoint paths between two nodes having minimum total length. |
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[40] | 308 | */ |
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| 309 | |
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[209] | 310 | /** |
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[314] | 311 | @defgroup max_flow Maximum Flow Algorithms |
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[209] | 312 | @ingroup algs |
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[50] | 313 | \brief Algorithms for finding maximum flows. |
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[40] | 314 | |
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[550] | 315 | This group contains the algorithms for finding maximum flows and |
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[40] | 316 | feasible circulations. |
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| 317 | |
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[406] | 318 | The \e maximum \e flow \e problem is to find a flow of maximum value between |
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| 319 | a single source and a single target. Formally, there is a \f$G=(V,A)\f$ |
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| 320 | digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and |
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| 321 | \f$s, t \in V\f$ source and target nodes. |
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| 322 | A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the |
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| 323 | following optimization problem. |
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[40] | 324 | |
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[406] | 325 | \f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f] |
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| 326 | \f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a) |
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| 327 | \qquad \forall v\in V\setminus\{s,t\} \f] |
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| 328 | \f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f] |
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[40] | 329 | |
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[50] | 330 | LEMON contains several algorithms for solving maximum flow problems: |
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[406] | 331 | - \ref EdmondsKarp Edmonds-Karp algorithm. |
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| 332 | - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm. |
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| 333 | - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. |
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| 334 | - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees. |
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[40] | 335 | |
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[406] | 336 | In most cases the \ref Preflow "Preflow" algorithm provides the |
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| 337 | fastest method for computing a maximum flow. All implementations |
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| 338 | provides functions to also query the minimum cut, which is the dual |
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| 339 | problem of the maximum flow. |
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[40] | 340 | */ |
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| 341 | |
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| 342 | /** |
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[314] | 343 | @defgroup min_cost_flow Minimum Cost Flow Algorithms |
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[40] | 344 | @ingroup algs |
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| 345 | |
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[50] | 346 | \brief Algorithms for finding minimum cost flows and circulations. |
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[40] | 347 | |
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[550] | 348 | This group contains the algorithms for finding minimum cost flows and |
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[209] | 349 | circulations. |
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[406] | 350 | |
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| 351 | The \e minimum \e cost \e flow \e problem is to find a feasible flow of |
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| 352 | minimum total cost from a set of supply nodes to a set of demand nodes |
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| 353 | in a network with capacity constraints and arc costs. |
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| 354 | Formally, let \f$G=(V,A)\f$ be a digraph, |
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| 355 | \f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and |
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| 356 | upper bounds for the flow values on the arcs, |
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| 357 | \f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow |
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| 358 | on the arcs, and |
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| 359 | \f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values |
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| 360 | of the nodes. |
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| 361 | A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of |
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| 362 | the following optimization problem. |
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| 363 | |
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| 364 | \f[ \min\sum_{a\in A} f(a) cost(a) \f] |
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| 365 | \f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) = |
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| 366 | supply(v) \qquad \forall v\in V \f] |
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| 367 | \f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f] |
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| 368 | |
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| 369 | LEMON contains several algorithms for solving minimum cost flow problems: |
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| 370 | - \ref CycleCanceling Cycle-canceling algorithms. |
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| 371 | - \ref CapacityScaling Successive shortest path algorithm with optional |
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| 372 | capacity scaling. |
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| 373 | - \ref CostScaling Push-relabel and augment-relabel algorithms based on |
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| 374 | cost scaling. |
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| 375 | - \ref NetworkSimplex Primal network simplex algorithm with various |
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| 376 | pivot strategies. |
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[40] | 377 | */ |
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| 378 | |
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| 379 | /** |
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[314] | 380 | @defgroup min_cut Minimum Cut Algorithms |
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[209] | 381 | @ingroup algs |
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[40] | 382 | |
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[50] | 383 | \brief Algorithms for finding minimum cut in graphs. |
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[40] | 384 | |
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[550] | 385 | This group contains the algorithms for finding minimum cut in graphs. |
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[40] | 386 | |
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[406] | 387 | The \e minimum \e cut \e problem is to find a non-empty and non-complete |
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| 388 | \f$X\f$ subset of the nodes with minimum overall capacity on |
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| 389 | outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a |
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| 390 | \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum |
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[50] | 391 | cut is the \f$X\f$ solution of the next optimization problem: |
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[40] | 392 | |
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[210] | 393 | \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} |
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[406] | 394 | \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] |
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[40] | 395 | |
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[50] | 396 | LEMON contains several algorithms related to minimum cut problems: |
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[40] | 397 | |
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[406] | 398 | - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut |
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| 399 | in directed graphs. |
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| 400 | - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for |
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| 401 | calculating minimum cut in undirected graphs. |
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[550] | 402 | - \ref GomoryHu "Gomory-Hu tree computation" for calculating |
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[406] | 403 | all-pairs minimum cut in undirected graphs. |
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[40] | 404 | |
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| 405 | If you want to find minimum cut just between two distinict nodes, |
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[406] | 406 | see the \ref max_flow "maximum flow problem". |
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[40] | 407 | */ |
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| 408 | |
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| 409 | /** |
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[578] | 410 | @defgroup graph_properties Connectivity and Other Graph Properties |
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[40] | 411 | @ingroup algs |
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[50] | 412 | \brief Algorithms for discovering the graph properties |
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[40] | 413 | |
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[550] | 414 | This group contains the algorithms for discovering the graph properties |
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[50] | 415 | like connectivity, bipartiteness, euler property, simplicity etc. |
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[40] | 416 | |
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| 417 | \image html edge_biconnected_components.png |
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| 418 | \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
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| 419 | */ |
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| 420 | |
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| 421 | /** |
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[314] | 422 | @defgroup planar Planarity Embedding and Drawing |
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[40] | 423 | @ingroup algs |
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[50] | 424 | \brief Algorithms for planarity checking, embedding and drawing |
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[40] | 425 | |
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[550] | 426 | This group contains the algorithms for planarity checking, |
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[210] | 427 | embedding and drawing. |
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[40] | 428 | |
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| 429 | \image html planar.png |
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| 430 | \image latex planar.eps "Plane graph" width=\textwidth |
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| 431 | */ |
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| 432 | |
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| 433 | /** |
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[314] | 434 | @defgroup matching Matching Algorithms |
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[40] | 435 | @ingroup algs |
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[50] | 436 | \brief Algorithms for finding matchings in graphs and bipartite graphs. |
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[40] | 437 | |
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[50] | 438 | This group contains algorithm objects and functions to calculate |
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[40] | 439 | matchings in graphs and bipartite graphs. The general matching problem is |
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[83] | 440 | finding a subset of the arcs which does not shares common endpoints. |
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[209] | 441 | |
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[40] | 442 | There are several different algorithms for calculate matchings in |
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| 443 | graphs. The matching problems in bipartite graphs are generally |
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| 444 | easier than in general graphs. The goal of the matching optimization |
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[406] | 445 | can be finding maximum cardinality, maximum weight or minimum cost |
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[40] | 446 | matching. The search can be constrained to find perfect or |
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| 447 | maximum cardinality matching. |
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| 448 | |
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[406] | 449 | The matching algorithms implemented in LEMON: |
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| 450 | - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm |
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| 451 | for calculating maximum cardinality matching in bipartite graphs. |
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| 452 | - \ref PrBipartiteMatching Push-relabel algorithm |
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| 453 | for calculating maximum cardinality matching in bipartite graphs. |
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| 454 | - \ref MaxWeightedBipartiteMatching |
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| 455 | Successive shortest path algorithm for calculating maximum weighted |
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| 456 | matching and maximum weighted bipartite matching in bipartite graphs. |
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| 457 | - \ref MinCostMaxBipartiteMatching |
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| 458 | Successive shortest path algorithm for calculating minimum cost maximum |
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| 459 | matching in bipartite graphs. |
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| 460 | - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating |
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| 461 | maximum cardinality matching in general graphs. |
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| 462 | - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating |
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| 463 | maximum weighted matching in general graphs. |
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| 464 | - \ref MaxWeightedPerfectMatching |
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| 465 | Edmond's blossom shrinking algorithm for calculating maximum weighted |
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| 466 | perfect matching in general graphs. |
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[40] | 467 | |
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| 468 | \image html bipartite_matching.png |
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| 469 | \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth |
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| 470 | */ |
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| 471 | |
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| 472 | /** |
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[314] | 473 | @defgroup spantree Minimum Spanning Tree Algorithms |
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[40] | 474 | @ingroup algs |
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[50] | 475 | \brief Algorithms for finding a minimum cost spanning tree in a graph. |
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[40] | 476 | |
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[550] | 477 | This group contains the algorithms for finding a minimum cost spanning |
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[406] | 478 | tree in a graph. |
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[40] | 479 | */ |
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| 480 | |
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| 481 | /** |
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[314] | 482 | @defgroup auxalg Auxiliary Algorithms |
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[40] | 483 | @ingroup algs |
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[50] | 484 | \brief Auxiliary algorithms implemented in LEMON. |
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[40] | 485 | |
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[550] | 486 | This group contains some algorithms implemented in LEMON |
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[50] | 487 | in order to make it easier to implement complex algorithms. |
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[40] | 488 | */ |
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| 489 | |
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| 490 | /** |
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[314] | 491 | @defgroup approx Approximation Algorithms |
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| 492 | @ingroup algs |
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[50] | 493 | \brief Approximation algorithms. |
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[40] | 494 | |
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[550] | 495 | This group contains the approximation and heuristic algorithms |
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[50] | 496 | implemented in LEMON. |
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[40] | 497 | */ |
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| 498 | |
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| 499 | /** |
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| 500 | @defgroup gen_opt_group General Optimization Tools |
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[550] | 501 | \brief This group contains some general optimization frameworks |
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[40] | 502 | implemented in LEMON. |
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| 503 | |
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[550] | 504 | This group contains some general optimization frameworks |
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[40] | 505 | implemented in LEMON. |
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| 506 | */ |
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| 507 | |
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| 508 | /** |
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[314] | 509 | @defgroup lp_group Lp and Mip Solvers |
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[40] | 510 | @ingroup gen_opt_group |
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| 511 | \brief Lp and Mip solver interfaces for LEMON. |
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| 512 | |
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[550] | 513 | This group contains Lp and Mip solver interfaces for LEMON. The |
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[40] | 514 | various LP solvers could be used in the same manner with this |
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| 515 | interface. |
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| 516 | */ |
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| 517 | |
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[209] | 518 | /** |
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[314] | 519 | @defgroup lp_utils Tools for Lp and Mip Solvers |
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[40] | 520 | @ingroup lp_group |
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[50] | 521 | \brief Helper tools to the Lp and Mip solvers. |
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[40] | 522 | |
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| 523 | This group adds some helper tools to general optimization framework |
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| 524 | implemented in LEMON. |
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| 525 | */ |
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| 526 | |
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| 527 | /** |
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| 528 | @defgroup metah Metaheuristics |
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| 529 | @ingroup gen_opt_group |
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| 530 | \brief Metaheuristics for LEMON library. |
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| 531 | |
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[550] | 532 | This group contains some metaheuristic optimization tools. |
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[40] | 533 | */ |
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| 534 | |
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| 535 | /** |
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[209] | 536 | @defgroup utils Tools and Utilities |
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[50] | 537 | \brief Tools and utilities for programming in LEMON |
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[40] | 538 | |
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[50] | 539 | Tools and utilities for programming in LEMON. |
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[40] | 540 | */ |
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| 541 | |
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| 542 | /** |
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| 543 | @defgroup gutils Basic Graph Utilities |
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| 544 | @ingroup utils |
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[50] | 545 | \brief Simple basic graph utilities. |
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[40] | 546 | |
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[550] | 547 | This group contains some simple basic graph utilities. |
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[40] | 548 | */ |
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| 549 | |
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| 550 | /** |
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| 551 | @defgroup misc Miscellaneous Tools |
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| 552 | @ingroup utils |
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[50] | 553 | \brief Tools for development, debugging and testing. |
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| 554 | |
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[550] | 555 | This group contains several useful tools for development, |
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[40] | 556 | debugging and testing. |
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| 557 | */ |
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| 558 | |
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| 559 | /** |
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[314] | 560 | @defgroup timecount Time Measuring and Counting |
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[40] | 561 | @ingroup misc |
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[50] | 562 | \brief Simple tools for measuring the performance of algorithms. |
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| 563 | |
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[550] | 564 | This group contains simple tools for measuring the performance |
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[40] | 565 | of algorithms. |
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| 566 | */ |
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| 567 | |
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| 568 | /** |
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| 569 | @defgroup exceptions Exceptions |
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| 570 | @ingroup utils |
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[50] | 571 | \brief Exceptions defined in LEMON. |
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| 572 | |
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[550] | 573 | This group contains the exceptions defined in LEMON. |
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[40] | 574 | */ |
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| 575 | |
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| 576 | /** |
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| 577 | @defgroup io_group Input-Output |
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[50] | 578 | \brief Graph Input-Output methods |
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[40] | 579 | |
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[550] | 580 | This group contains the tools for importing and exporting graphs |
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[314] | 581 | and graph related data. Now it supports the \ref lgf-format |
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| 582 | "LEMON Graph Format", the \c DIMACS format and the encapsulated |
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| 583 | postscript (EPS) format. |
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[40] | 584 | */ |
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| 585 | |
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| 586 | /** |
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[351] | 587 | @defgroup lemon_io LEMON Graph Format |
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[40] | 588 | @ingroup io_group |
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[314] | 589 | \brief Reading and writing LEMON Graph Format. |
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[40] | 590 | |
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[550] | 591 | This group contains methods for reading and writing |
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[236] | 592 | \ref lgf-format "LEMON Graph Format". |
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[40] | 593 | */ |
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| 594 | |
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| 595 | /** |
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[314] | 596 | @defgroup eps_io Postscript Exporting |
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[40] | 597 | @ingroup io_group |
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| 598 | \brief General \c EPS drawer and graph exporter |
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| 599 | |
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[550] | 600 | This group contains general \c EPS drawing methods and special |
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[209] | 601 | graph exporting tools. |
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[40] | 602 | */ |
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| 603 | |
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| 604 | /** |
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[388] | 605 | @defgroup dimacs_group DIMACS format |
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| 606 | @ingroup io_group |
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| 607 | \brief Read and write files in DIMACS format |
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| 608 | |
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| 609 | Tools to read a digraph from or write it to a file in DIMACS format data. |
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| 610 | */ |
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| 611 | |
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| 612 | /** |
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[351] | 613 | @defgroup nauty_group NAUTY Format |
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| 614 | @ingroup io_group |
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| 615 | \brief Read \e Nauty format |
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[388] | 616 | |
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[351] | 617 | Tool to read graphs from \e Nauty format data. |
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| 618 | */ |
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| 619 | |
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| 620 | /** |
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[40] | 621 | @defgroup concept Concepts |
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| 622 | \brief Skeleton classes and concept checking classes |
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| 623 | |
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[550] | 624 | This group contains the data/algorithm skeletons and concept checking |
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[40] | 625 | classes implemented in LEMON. |
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| 626 | |
---|
| 627 | The purpose of the classes in this group is fourfold. |
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[209] | 628 | |
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[318] | 629 | - These classes contain the documentations of the %concepts. In order |
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[40] | 630 | to avoid document multiplications, an implementation of a concept |
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| 631 | simply refers to the corresponding concept class. |
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| 632 | |
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| 633 | - These classes declare every functions, <tt>typedef</tt>s etc. an |
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[318] | 634 | implementation of the %concepts should provide, however completely |
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[40] | 635 | without implementations and real data structures behind the |
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| 636 | interface. On the other hand they should provide nothing else. All |
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| 637 | the algorithms working on a data structure meeting a certain concept |
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| 638 | should compile with these classes. (Though it will not run properly, |
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| 639 | of course.) In this way it is easily to check if an algorithm |
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| 640 | doesn't use any extra feature of a certain implementation. |
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| 641 | |
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| 642 | - The concept descriptor classes also provide a <em>checker class</em> |
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[50] | 643 | that makes it possible to check whether a certain implementation of a |
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[40] | 644 | concept indeed provides all the required features. |
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| 645 | |
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| 646 | - Finally, They can serve as a skeleton of a new implementation of a concept. |
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| 647 | */ |
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| 648 | |
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| 649 | /** |
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| 650 | @defgroup graph_concepts Graph Structure Concepts |
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| 651 | @ingroup concept |
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| 652 | \brief Skeleton and concept checking classes for graph structures |
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| 653 | |
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[550] | 654 | This group contains the skeletons and concept checking classes of LEMON's |
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[40] | 655 | graph structures and helper classes used to implement these. |
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| 656 | */ |
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| 657 | |
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[314] | 658 | /** |
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| 659 | @defgroup map_concepts Map Concepts |
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| 660 | @ingroup concept |
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| 661 | \brief Skeleton and concept checking classes for maps |
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| 662 | |
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[550] | 663 | This group contains the skeletons and concept checking classes of maps. |
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[40] | 664 | */ |
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| 665 | |
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| 666 | /** |
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| 667 | \anchor demoprograms |
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| 668 | |
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[406] | 669 | @defgroup demos Demo Programs |
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[40] | 670 | |
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| 671 | Some demo programs are listed here. Their full source codes can be found in |
---|
| 672 | the \c demo subdirectory of the source tree. |
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| 673 | |
---|
[556] | 674 | In order to compile them, use the <tt>make demo</tt> or the |
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| 675 | <tt>make check</tt> commands. |
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[40] | 676 | */ |
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| 677 | |
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| 678 | /** |
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[406] | 679 | @defgroup tools Standalone Utility Applications |
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[40] | 680 | |
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[209] | 681 | Some utility applications are listed here. |
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[40] | 682 | |
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| 683 | The standard compilation procedure (<tt>./configure;make</tt>) will compile |
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[209] | 684 | them, as well. |
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[40] | 685 | */ |
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| 686 | |
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[406] | 687 | } |
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