diff --git a/doc/groups.dox b/doc/groups.dox --- a/doc/groups.dox +++ b/doc/groups.dox @@ -20,7 +20,7 @@ /** @defgroup datas Data Structures -This group describes the several data structures implemented in LEMON. +This group contains the several data structures implemented in LEMON. */ /** @@ -138,21 +138,11 @@ */ /** -@defgroup semi_adaptors Semi-Adaptor Classes for Graphs -@ingroup graphs -\brief Graph types between real graphs and graph adaptors. - -This group describes some graph types between real graphs and graph adaptors. -These classes wrap graphs to give new functionality as the adaptors do it. -On the other hand they are not light-weight structures as the adaptors. -*/ - -/** @defgroup maps Maps @ingroup datas \brief Map structures implemented in LEMON. -This group describes the map structures implemented in LEMON. +This group contains the map structures implemented in LEMON. LEMON provides several special purpose maps and map adaptors that e.g. combine new maps from existing ones. @@ -165,7 +155,7 @@ @ingroup maps \brief Special graph-related maps. -This group describes maps that are specifically designed to assign +This group contains maps that are specifically designed to assign values to the nodes and arcs/edges of graphs. If you are looking for the standard graph maps (\c NodeMap, \c ArcMap, @@ -177,7 +167,7 @@ \ingroup maps \brief Tools to create new maps from existing ones -This group describes map adaptors that are used to create "implicit" +This group contains map adaptors that are used to create "implicit" maps from other maps. Most of them are \ref concepts::ReadMap "read-only maps". @@ -236,19 +226,11 @@ */ /** -@defgroup matrices Matrices -@ingroup datas -\brief Two dimensional data storages implemented in LEMON. - -This group describes two dimensional data storages implemented in LEMON. -*/ - -/** @defgroup paths Path Structures @ingroup datas \brief %Path structures implemented in LEMON. -This group describes the path structures implemented in LEMON. +This group contains the path structures implemented in LEMON. LEMON provides flexible data structures to work with paths. All of them have similar interfaces and they can be copied easily with @@ -256,7 +238,36 @@ efficient to have e.g. the Dijkstra algorithm to store its result in any kind of path structure. -\sa lemon::concepts::Path +\sa \ref concepts::Path "Path concept" +*/ + +/** +@defgroup heaps Heap Structures +@ingroup datas +\brief %Heap structures implemented in LEMON. + +This group contains the heap structures implemented in LEMON. + +LEMON provides several heap classes. They are efficient implementations +of the abstract data type \e priority \e queue. They store items with +specified values called \e priorities in such a way that finding and +removing the item with minimum priority are efficient. +The basic operations are adding and erasing items, changing the priority +of an item, etc. + +Heaps are crucial in several algorithms, such as Dijkstra and Prim. +The heap implementations have the same interface, thus any of them can be +used easily in such algorithms. + +\sa \ref concepts::Heap "Heap concept" +*/ + +/** +@defgroup matrices Matrices +@ingroup datas +\brief Two dimensional data storages implemented in LEMON. + +This group contains two dimensional data storages implemented in LEMON. */ /** @@ -264,16 +275,38 @@ @ingroup datas \brief Auxiliary data structures implemented in LEMON. -This group describes some data structures implemented in LEMON in +This group contains some data structures implemented in LEMON in order to make it easier to implement combinatorial algorithms. */ /** +@defgroup geomdat Geometric Data Structures +@ingroup auxdat +\brief Geometric data structures implemented in LEMON. + +This group contains geometric data structures implemented in LEMON. + + - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional + vector with the usual operations. + - \ref lemon::dim2::Box "dim2::Box" can be used to determine the + rectangular bounding box of a set of \ref lemon::dim2::Point + "dim2::Point"'s. +*/ + +/** +@defgroup matrices Matrices +@ingroup auxdat +\brief Two dimensional data storages implemented in LEMON. + +This group contains two dimensional data storages implemented in LEMON. +*/ + +/** @defgroup algs Algorithms -\brief This group describes the several algorithms +\brief This group contains the several algorithms implemented in LEMON. -This group describes the several algorithms +This group contains the several algorithms implemented in LEMON. */ @@ -282,8 +315,9 @@ @ingroup algs \brief Common graph search algorithms. -This group describes the common graph search algorithms, namely -\e breadth-first \e search (BFS) and \e depth-first \e search (DFS). +This group contains the common graph search algorithms, namely +\e breadth-first \e search (BFS) and \e depth-first \e search (DFS) +\ref clrs01algorithms. */ /** @@ -291,7 +325,8 @@ @ingroup algs \brief Algorithms for finding shortest paths. -This group describes the algorithms for finding shortest paths in digraphs. +This group contains the algorithms for finding shortest paths in digraphs +\ref clrs01algorithms. - \ref Dijkstra algorithm for finding shortest paths from a source node when all arc lengths are non-negative. @@ -308,72 +343,83 @@ */ /** +@defgroup spantree Minimum Spanning Tree Algorithms +@ingroup algs +\brief Algorithms for finding minimum cost spanning trees and arborescences. + +This group contains the algorithms for finding minimum cost spanning +trees and arborescences \ref clrs01algorithms. +*/ + +/** @defgroup max_flow Maximum Flow Algorithms @ingroup algs \brief Algorithms for finding maximum flows. -This group describes the algorithms for finding maximum flows and -feasible circulations. +This group contains the algorithms for finding maximum flows and +feasible circulations \ref clrs01algorithms, \ref amo93networkflows. The \e maximum \e flow \e problem is to find a flow of maximum value between a single source and a single target. Formally, there is a \f$G=(V,A)\f$ -digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and +digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and \f$s, t \in V\f$ source and target nodes. -A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the +A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the following optimization problem. -\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f] -\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a) - \qquad \forall v\in V\setminus\{s,t\} \f] -\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f] +\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f] +\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu) + \quad \forall u\in V\setminus\{s,t\} \f] +\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] LEMON contains several algorithms for solving maximum flow problems: -- \ref EdmondsKarp Edmonds-Karp algorithm. -- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm. -- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. -- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees. +- \ref EdmondsKarp Edmonds-Karp algorithm + \ref edmondskarp72theoretical. +- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm + \ref goldberg88newapproach. +- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees + \ref dinic70algorithm, \ref sleator83dynamic. +- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees + \ref goldberg88newapproach, \ref sleator83dynamic. -In most cases the \ref Preflow "Preflow" algorithm provides the +In most cases the \ref Preflow algorithm provides the fastest method for computing a maximum flow. All implementations -provides functions to also query the minimum cut, which is the dual -problem of the maximum flow. +also provide functions to query the minimum cut, which is the dual +problem of maximum flow. + +\ref Circulation is a preflow push-relabel algorithm implemented directly +for finding feasible circulations, which is a somewhat different problem, +but it is strongly related to maximum flow. +For more information, see \ref Circulation. */ /** -@defgroup min_cost_flow Minimum Cost Flow Algorithms +@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms @ingroup algs \brief Algorithms for finding minimum cost flows and circulations. -This group describes the algorithms for finding minimum cost flows and -circulations. +This group contains the algorithms for finding minimum cost flows and +circulations \ref amo93networkflows. For more information about this +problem and its dual solution, see \ref min_cost_flow +"Minimum Cost Flow Problem". -The \e minimum \e cost \e flow \e problem is to find a feasible flow of -minimum total cost from a set of supply nodes to a set of demand nodes -in a network with capacity constraints and arc costs. -Formally, let \f$G=(V,A)\f$ be a digraph, -\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and -upper bounds for the flow values on the arcs, -\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow -on the arcs, and -\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values -of the nodes. -A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of -the following optimization problem. +LEMON contains several algorithms for this problem. + - \ref NetworkSimplex Primal Network Simplex algorithm with various + pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. + - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on + cost scaling \ref goldberg90approximation, \ref goldberg97efficient, + \ref bunnagel98efficient. + - \ref CapacityScaling Successive Shortest %Path algorithm with optional + capacity scaling \ref edmondskarp72theoretical. + - \ref CancelAndTighten The Cancel and Tighten algorithm + \ref goldberg89cyclecanceling. + - \ref CycleCanceling Cycle-Canceling algorithms + \ref klein67primal, \ref goldberg89cyclecanceling. -\f[ \min\sum_{a\in A} f(a) cost(a) \f] -\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) = - supply(v) \qquad \forall v\in V \f] -\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f] - -LEMON contains several algorithms for solving minimum cost flow problems: - - \ref CycleCanceling Cycle-canceling algorithms. - - \ref CapacityScaling Successive shortest path algorithm with optional - capacity scaling. - - \ref CostScaling Push-relabel and augment-relabel algorithms based on - cost scaling. - - \ref NetworkSimplex Primal network simplex algorithm with various - pivot strategies. +In general NetworkSimplex is the most efficient implementation, +but in special cases other algorithms could be faster. +For example, if the total supply and/or capacities are rather small, +CapacityScaling is usually the fastest algorithm (without effective scaling). */ /** @@ -382,7 +428,7 @@ \brief Algorithms for finding minimum cut in graphs. -This group describes the algorithms for finding minimum cut in graphs. +This group contains the algorithms for finding minimum cut in graphs. The \e minimum \e cut \e problem is to find a non-empty and non-complete \f$X\f$ subset of the nodes with minimum overall capacity on @@ -391,7 +437,7 @@ cut is the \f$X\f$ solution of the next optimization problem: \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} - \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] + \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f] LEMON contains several algorithms related to minimum cut problems: @@ -399,7 +445,7 @@ in directed graphs. - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for calculating minimum cut in undirected graphs. -- \ref GomoryHuTree "Gomory-Hu tree computation" for calculating +- \ref GomoryHu "Gomory-Hu tree computation" for calculating all-pairs minimum cut in undirected graphs. If you want to find minimum cut just between two distinict nodes, @@ -407,27 +453,40 @@ */ /** -@defgroup graph_prop Connectivity and Other Graph Properties +@defgroup min_mean_cycle Minimum Mean Cycle Algorithms @ingroup algs -\brief Algorithms for discovering the graph properties +\brief Algorithms for finding minimum mean cycles. -This group describes the algorithms for discovering the graph properties -like connectivity, bipartiteness, euler property, simplicity etc. +This group contains the algorithms for finding minimum mean cycles +\ref clrs01algorithms, \ref amo93networkflows. -\image html edge_biconnected_components.png -\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth -*/ +The \e minimum \e mean \e cycle \e problem is to find a directed cycle +of minimum mean length (cost) in a digraph. +The mean length of a cycle is the average length of its arcs, i.e. the +ratio between the total length of the cycle and the number of arcs on it. -/** -@defgroup planar Planarity Embedding and Drawing -@ingroup algs -\brief Algorithms for planarity checking, embedding and drawing +This problem has an important connection to \e conservative \e length +\e functions, too. A length function on the arcs of a digraph is called +conservative if and only if there is no directed cycle of negative total +length. For an arbitrary length function, the negative of the minimum +cycle mean is the smallest \f$\epsilon\f$ value so that increasing the +arc lengths uniformly by \f$\epsilon\f$ results in a conservative length +function. -This group describes the algorithms for planarity checking, -embedding and drawing. +LEMON contains three algorithms for solving the minimum mean cycle problem: +- \ref Karp "Karp"'s original algorithm \ref amo93networkflows, + \ref dasdan98minmeancycle. +- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved + version of Karp's algorithm \ref dasdan98minmeancycle. +- \ref Howard "Howard"'s policy iteration algorithm + \ref dasdan98minmeancycle. -\image html planar.png -\image latex planar.eps "Plane graph" width=\textwidth +In practice, the Howard algorithm proved to be by far the most efficient +one, though the best known theoretical bound on its running time is +exponential. +Both Karp and HartmannOrlin algorithms run in time O(ne) and use space +O(n2+e), but the latter one is typically faster due to the +applied early termination scheme. */ /** @@ -435,9 +494,10 @@ @ingroup algs \brief Algorithms for finding matchings in graphs and bipartite graphs. -This group contains algorithm objects and functions to calculate +This group contains the algorithms for calculating matchings in graphs and bipartite graphs. The general matching problem is -finding a subset of the arcs which does not shares common endpoints. +finding a subset of the edges for which each node has at most one incident +edge. There are several different algorithms for calculate matchings in graphs. The matching problems in bipartite graphs are generally @@ -470,12 +530,36 @@ */ /** -@defgroup spantree Minimum Spanning Tree Algorithms +@defgroup graph_properties Connectivity and Other Graph Properties @ingroup algs -\brief Algorithms for finding a minimum cost spanning tree in a graph. +\brief Algorithms for discovering the graph properties -This group describes the algorithms for finding a minimum cost spanning -tree in a graph. +This group contains the algorithms for discovering the graph properties +like connectivity, bipartiteness, euler property, simplicity etc. + +\image html connected_components.png +\image latex connected_components.eps "Connected components" width=\textwidth +*/ + +/** +@defgroup planar Planarity Embedding and Drawing +@ingroup algs +\brief Algorithms for planarity checking, embedding and drawing + +This group contains the algorithms for planarity checking, +embedding and drawing. + +\image html planar.png +\image latex planar.eps "Plane graph" width=\textwidth +*/ + +/** +@defgroup approx Approximation Algorithms +@ingroup algs +\brief Approximation algorithms. + +This group contains the approximation and heuristic algorithms +implemented in LEMON. */ /** @@ -483,36 +567,30 @@ @ingroup algs \brief Auxiliary algorithms implemented in LEMON. -This group describes some algorithms implemented in LEMON +This group contains some algorithms implemented in LEMON in order to make it easier to implement complex algorithms. */ /** -@defgroup approx Approximation Algorithms -@ingroup algs -\brief Approximation algorithms. +@defgroup gen_opt_group General Optimization Tools +\brief This group contains some general optimization frameworks +implemented in LEMON. -This group describes the approximation and heuristic algorithms +This group contains some general optimization frameworks implemented in LEMON. */ /** -@defgroup gen_opt_group General Optimization Tools -\brief This group describes some general optimization frameworks -implemented in LEMON. +@defgroup lp_group LP and MIP Solvers +@ingroup gen_opt_group +\brief LP and MIP solver interfaces for LEMON. -This group describes some general optimization frameworks -implemented in LEMON. -*/ +This group contains LP and MIP solver interfaces for LEMON. +Various LP solvers could be used in the same manner with this +high-level interface. -/** -@defgroup lp_group Lp and Mip Solvers -@ingroup gen_opt_group -\brief Lp and Mip solver interfaces for LEMON. - -This group describes Lp and Mip solver interfaces for LEMON. The -various LP solvers could be used in the same manner with this -interface. +The currently supported solvers are \ref glpk, \ref clp, \ref cbc, +\ref cplex, \ref soplex. */ /** @@ -529,7 +607,7 @@ @ingroup gen_opt_group \brief Metaheuristics for LEMON library. -This group describes some metaheuristic optimization tools. +This group contains some metaheuristic optimization tools. */ /** @@ -544,7 +622,7 @@ @ingroup utils \brief Simple basic graph utilities. -This group describes some simple basic graph utilities. +This group contains some simple basic graph utilities. */ /** @@ -552,7 +630,7 @@ @ingroup utils \brief Tools for development, debugging and testing. -This group describes several useful tools for development, +This group contains several useful tools for development, debugging and testing. */ @@ -561,7 +639,7 @@ @ingroup misc \brief Simple tools for measuring the performance of algorithms. -This group describes simple tools for measuring the performance +This group contains simple tools for measuring the performance of algorithms. */ @@ -570,14 +648,14 @@ @ingroup utils \brief Exceptions defined in LEMON. -This group describes the exceptions defined in LEMON. +This group contains the exceptions defined in LEMON. */ /** @defgroup io_group Input-Output \brief Graph Input-Output methods -This group describes the tools for importing and exporting graphs +This group contains the tools for importing and exporting graphs and graph related data. Now it supports the \ref lgf-format "LEMON Graph Format", the \c DIMACS format and the encapsulated postscript (EPS) format. @@ -588,7 +666,7 @@ @ingroup io_group \brief Reading and writing LEMON Graph Format. -This group describes methods for reading and writing +This group contains methods for reading and writing \ref lgf-format "LEMON Graph Format". */ @@ -597,12 +675,12 @@ @ingroup io_group \brief General \c EPS drawer and graph exporter -This group describes general \c EPS drawing methods and special +This group contains general \c EPS drawing methods and special graph exporting tools. */ /** -@defgroup dimacs_group DIMACS format +@defgroup dimacs_group DIMACS Format @ingroup io_group \brief Read and write files in DIMACS format @@ -621,7 +699,7 @@ @defgroup concept Concepts \brief Skeleton classes and concept checking classes -This group describes the data/algorithm skeletons and concept checking +This group contains the data/algorithm skeletons and concept checking classes implemented in LEMON. The purpose of the classes in this group is fourfold. @@ -651,8 +729,8 @@ @ingroup concept \brief Skeleton and concept checking classes for graph structures -This group describes the skeletons and concept checking classes of LEMON's -graph structures and helper classes used to implement these. +This group contains the skeletons and concept checking classes of +graph structures. */ /** @@ -660,19 +738,7 @@ @ingroup concept \brief Skeleton and concept checking classes for maps -This group describes the skeletons and concept checking classes of maps. -*/ - -/** -\anchor demoprograms - -@defgroup demos Demo Programs - -Some demo programs are listed here. Their full source codes can be found in -the \c demo subdirectory of the source tree. - -It order to compile them, use --enable-demo configure option when -build the library. +This group contains the skeletons and concept checking classes of maps. */ /** @@ -684,4 +750,16 @@ them, as well. */ +/** +\anchor demoprograms + +@defgroup demos Demo Programs + +Some demo programs are listed here. Their full source codes can be found in +the \c demo subdirectory of the source tree. + +In order to compile them, use the make demo or the +make check commands. +*/ + }