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This group contains two dimensional data storages implemented in LEMON.
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*/
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/**
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@defgroup auxdat Auxiliary Data Structures
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@ingroup datas
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\brief Auxiliary data structures implemented in LEMON.
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This group contains some data structures implemented in LEMON in
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order to make it easier to implement combinatorial algorithms.
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*/
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/**
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@defgroup geomdat Geometric Data Structures
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@ingroup auxdat
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\brief Geometric data structures implemented in LEMON.
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This group contains geometric data structures implemented in LEMON.
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- \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
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vector with the usual operations.
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- \ref lemon::dim2::Box "dim2::Box" can be used to determine the
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rectangular bounding box of a set of \ref lemon::dim2::Point
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"dim2::Point"'s.
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*/
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/**
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@defgroup matrices Matrices
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@ingroup auxdat
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\brief Two dimensional data storages implemented in LEMON.
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This group contains two dimensional data storages implemented in LEMON.
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*/
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|
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/**
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@defgroup algs Algorithms
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\brief This group contains the several algorithms
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implemented in LEMON.
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This group contains the several algorithms
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implemented in LEMON.
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*/
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/**
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@defgroup search Graph Search
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@ingroup algs
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\brief Common graph search algorithms.
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This group contains the common graph search algorithms, namely
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\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
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\ref clrs01algorithms.
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*/
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/**
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@defgroup shortest_path Shortest Path Algorithms
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@ingroup algs
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\brief Algorithms for finding shortest paths.
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This group contains the algorithms for finding shortest paths in digraphs
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\ref clrs01algorithms.
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- \ref Dijkstra algorithm for finding shortest paths from a source node
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when all arc lengths are non-negative.
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- \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
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from a source node when arc lenghts can be either positive or negative,
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but the digraph should not contain directed cycles with negative total
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length.
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- \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
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for solving the \e all-pairs \e shortest \e paths \e problem when arc
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lenghts can be either positive or negative, but the digraph should
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not contain directed cycles with negative total length.
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- \ref Suurballe A successive shortest path algorithm for finding
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arc-disjoint paths between two nodes having minimum total length.
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*/
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/**
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@defgroup spantree Minimum Spanning Tree Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cost spanning trees and arborescences.
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This group contains the algorithms for finding minimum cost spanning
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trees and arborescences \ref clrs01algorithms.
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*/
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/**
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@defgroup max_flow Maximum Flow Algorithms
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@ingroup algs
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\brief Algorithms for finding maximum flows.
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This group contains the algorithms for finding maximum flows and
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feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
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The \e maximum \e flow \e problem is to find a flow of maximum value between
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a single source and a single target. Formally, there is a \f$G=(V,A)\f$
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digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
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\f$s, t \in V\f$ source and target nodes.
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A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
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following optimization problem.
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\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
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\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
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\quad \forall u\in V\setminus\{s,t\} \f]
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\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
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LEMON contains several algorithms for solving maximum flow problems:
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- \ref EdmondsKarp Edmonds-Karp algorithm
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\ref edmondskarp72theoretical.
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- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
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\ref goldberg88newapproach.
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- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
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\ref dinic70algorithm, \ref sleator83dynamic.
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- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
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\ref goldberg88newapproach, \ref sleator83dynamic.
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In most cases the \ref Preflow algorithm provides the
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fastest method for computing a maximum flow. All implementations
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also provide functions to query the minimum cut, which is the dual
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problem of maximum flow.
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\ref Circulation is a preflow push-relabel algorithm implemented directly
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for finding feasible circulations, which is a somewhat different problem,
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but it is strongly related to maximum flow.
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For more information, see \ref Circulation.
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*/
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/**
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@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cost flows and circulations.
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This group contains the algorithms for finding minimum cost flows and
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circulations \ref amo93networkflows. For more information about this
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problem and its dual solution, see \ref min_cost_flow
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"Minimum Cost Flow Problem".
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LEMON contains several algorithms for this problem.
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- \ref NetworkSimplex Primal Network Simplex algorithm with various
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pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
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- \ref CostScaling Cost Scaling algorithm based on push/augment and
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relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
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\ref bunnagel98efficient.
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- \ref CapacityScaling Capacity Scaling algorithm based on the successive
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shortest path method \ref edmondskarp72theoretical.
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- \ref CycleCanceling Cycle-Canceling algorithms, two of which are
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strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
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In general NetworkSimplex is the most efficient implementation,
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but in special cases other algorithms could be faster.
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For example, if the total supply and/or capacities are rather small,
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CapacityScaling is usually the fastest algorithm (without effective scaling).
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*/
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/**
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@defgroup min_cut Minimum Cut Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cut in graphs.
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This group contains the algorithms for finding minimum cut in graphs.
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The \e minimum \e cut \e problem is to find a non-empty and non-complete
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\f$X\f$ subset of the nodes with minimum overall capacity on
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outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
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\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
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cut is the \f$X\f$ solution of the next optimization problem:
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\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
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\sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
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LEMON contains several algorithms related to minimum cut problems:
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- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
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in directed graphs.
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- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
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calculating minimum cut in undirected graphs.
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- \ref GomoryHu "Gomory-Hu tree computation" for calculating
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all-pairs minimum cut in undirected graphs.
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If you want to find minimum cut just between two distinict nodes,
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see the \ref max_flow "maximum flow problem".
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*/
|
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|
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/**
|
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@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum mean cycles.
|
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457 |
|
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This group contains the algorithms for finding minimum mean cycles
|
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\ref clrs01algorithms, \ref amo93networkflows.
|
460 |
460 |
|
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461 |
The \e minimum \e mean \e cycle \e problem is to find a directed cycle
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of minimum mean length (cost) in a digraph.
|
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The mean length of a cycle is the average length of its arcs, i.e. the
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ratio between the total length of the cycle and the number of arcs on it.
|
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This problem has an important connection to \e conservative \e length
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\e functions, too. A length function on the arcs of a digraph is called
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conservative if and only if there is no directed cycle of negative total
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length. For an arbitrary length function, the negative of the minimum
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cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
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arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
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function.
|
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LEMON contains three algorithms for solving the minimum mean cycle problem:
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- \ref Karp "Karp"'s original algorithm \ref amo93networkflows,
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\ref dasdan98minmeancycle.
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- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
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version of Karp's algorithm \ref dasdan98minmeancycle.
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- \ref Howard "Howard"'s policy iteration algorithm
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\ref dasdan98minmeancycle.
|
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|
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In practice, the Howard algorithm proved to be by far the most efficient
|
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one, though the best known theoretical bound on its running time is
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exponential.
|
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Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
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O(n<sup>2</sup>+e), but the latter one is typically faster due to the
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applied early termination scheme.
|
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*/
|
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|
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/**
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@defgroup matching Matching Algorithms
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@ingroup algs
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\brief Algorithms for finding matchings in graphs and bipartite graphs.
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|
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This group contains the algorithms for calculating
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matchings in graphs and bipartite graphs. The general matching problem is
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finding a subset of the edges for which each node has at most one incident
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edge.
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There are several different algorithms for calculate matchings in
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graphs. The matching problems in bipartite graphs are generally
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easier than in general graphs. The goal of the matching optimization
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can be finding maximum cardinality, maximum weight or minimum cost
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matching. The search can be constrained to find perfect or
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maximum cardinality matching.
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The matching algorithms implemented in LEMON:
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- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
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for calculating maximum cardinality matching in bipartite graphs.
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- \ref PrBipartiteMatching Push-relabel algorithm
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for calculating maximum cardinality matching in bipartite graphs.
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- \ref MaxWeightedBipartiteMatching
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Successive shortest path algorithm for calculating maximum weighted
|
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matching and maximum weighted bipartite matching in bipartite graphs.
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- \ref MinCostMaxBipartiteMatching
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Successive shortest path algorithm for calculating minimum cost maximum
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matching in bipartite graphs.
|
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- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
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maximum cardinality matching in general graphs.
|
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- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
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maximum weighted matching in general graphs.
|
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522 |
- \ref MaxWeightedPerfectMatching
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Edmond's blossom shrinking algorithm for calculating maximum weighted
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perfect matching in general graphs.
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|
\image html bipartite_matching.png
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\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
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\image html matching.png
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\image latex matching.eps "Bipartite Matching" width=\textwidth
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*/
|
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/**
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@defgroup graph_properties Connectivity and Other Graph Properties
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@ingroup algs
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\brief Algorithms for discovering the graph properties
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This group contains the algorithms for discovering the graph properties
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like connectivity, bipartiteness, euler property, simplicity etc.
|
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537 |
|
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\image html connected_components.png
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\image latex connected_components.eps "Connected components" width=\textwidth
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*/
|
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541 |
|
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/**
|
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@defgroup planar Planarity Embedding and Drawing
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@ingroup algs
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\brief Algorithms for planarity checking, embedding and drawing
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546 |
|
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This group contains the algorithms for planarity checking,
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embedding and drawing.
|
549 |
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|
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\image html planar.png
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\image latex planar.eps "Plane graph" width=\textwidth
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*/
|
553 |
553 |
|
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/**
|
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@defgroup approx Approximation Algorithms
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@ingroup algs
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\brief Approximation algorithms.
|
558 |
558 |
|
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559 |
This group contains the approximation and heuristic algorithms
|
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implemented in LEMON.
|
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561 |
*/
|
562 |
562 |
|
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563 |
/**
|
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564 |
@defgroup auxalg Auxiliary Algorithms
|
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565 |
@ingroup algs
|
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566 |
\brief Auxiliary algorithms implemented in LEMON.
|
567 |
567 |
|
568 |
568 |
This group contains some algorithms implemented in LEMON
|
569 |
569 |
in order to make it easier to implement complex algorithms.
|
570 |
570 |
*/
|
571 |
571 |
|
572 |
572 |
/**
|
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573 |
@defgroup gen_opt_group General Optimization Tools
|
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\brief This group contains some general optimization frameworks
|
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575 |
implemented in LEMON.
|
576 |
576 |
|
577 |
577 |
This group contains some general optimization frameworks
|
578 |
578 |
implemented in LEMON.
|
579 |
579 |
*/
|
580 |
580 |
|
581 |
581 |
/**
|
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@defgroup lp_group LP and MIP Solvers
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@ingroup gen_opt_group
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584 |
\brief LP and MIP solver interfaces for LEMON.
|
585 |
585 |
|
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586 |
This group contains LP and MIP solver interfaces for LEMON.
|
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587 |
Various LP solvers could be used in the same manner with this
|
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high-level interface.
|
589 |
589 |
|
590 |
590 |
The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
|
591 |
591 |
\ref cplex, \ref soplex.
|
592 |
592 |
*/
|
593 |
593 |
|
594 |
594 |
/**
|
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595 |
@defgroup lp_utils Tools for Lp and Mip Solvers
|
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596 |
@ingroup lp_group
|
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597 |
\brief Helper tools to the Lp and Mip solvers.
|
598 |
598 |
|
599 |
599 |
This group adds some helper tools to general optimization framework
|
600 |
600 |
implemented in LEMON.
|
601 |
601 |
*/
|
602 |
602 |
|
603 |
603 |
/**
|
604 |
604 |
@defgroup metah Metaheuristics
|
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605 |
@ingroup gen_opt_group
|
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606 |
\brief Metaheuristics for LEMON library.
|
607 |
607 |
|
608 |
608 |
This group contains some metaheuristic optimization tools.
|
609 |
609 |
*/
|
610 |
610 |
|
611 |
611 |
/**
|
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612 |
@defgroup utils Tools and Utilities
|
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613 |
\brief Tools and utilities for programming in LEMON
|
614 |
614 |
|
615 |
615 |
Tools and utilities for programming in LEMON.
|
616 |
616 |
*/
|
617 |
617 |
|
618 |
618 |
/**
|
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619 |
@defgroup gutils Basic Graph Utilities
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620 |
@ingroup utils
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621 |
\brief Simple basic graph utilities.
|
622 |
622 |
|
623 |
623 |
This group contains some simple basic graph utilities.
|
624 |
624 |
*/
|
625 |
625 |
|
626 |
626 |
/**
|
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627 |
@defgroup misc Miscellaneous Tools
|
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628 |
@ingroup utils
|
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\brief Tools for development, debugging and testing.
|
630 |
630 |
|
631 |
631 |
This group contains several useful tools for development,
|
632 |
632 |
debugging and testing.
|
633 |
633 |
*/
|
634 |
634 |
|
635 |
635 |
/**
|
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636 |
@defgroup timecount Time Measuring and Counting
|
637 |
637 |
@ingroup misc
|
638 |
638 |
\brief Simple tools for measuring the performance of algorithms.
|
639 |
639 |
|
640 |
640 |
This group contains simple tools for measuring the performance
|
641 |
641 |
of algorithms.
|
642 |
642 |
*/
|
643 |
643 |
|
644 |
644 |
/**
|
645 |
645 |
@defgroup exceptions Exceptions
|
646 |
646 |
@ingroup utils
|
647 |
647 |
\brief Exceptions defined in LEMON.
|
648 |
648 |
|
649 |
649 |
This group contains the exceptions defined in LEMON.
|
650 |
650 |
*/
|
651 |
651 |
|
652 |
652 |
/**
|
653 |
653 |
@defgroup io_group Input-Output
|
654 |
654 |
\brief Graph Input-Output methods
|
655 |
655 |
|
656 |
656 |
This group contains the tools for importing and exporting graphs
|
657 |
657 |
and graph related data. Now it supports the \ref lgf-format
|
658 |
658 |
"LEMON Graph Format", the \c DIMACS format and the encapsulated
|
659 |
659 |
postscript (EPS) format.
|
660 |
660 |
*/
|
661 |
661 |
|
662 |
662 |
/**
|
663 |
663 |
@defgroup lemon_io LEMON Graph Format
|
664 |
664 |
@ingroup io_group
|
665 |
665 |
\brief Reading and writing LEMON Graph Format.
|
666 |
666 |
|
667 |
667 |
This group contains methods for reading and writing
|
668 |
668 |
\ref lgf-format "LEMON Graph Format".
|
669 |
669 |
*/
|
670 |
670 |
|
671 |
671 |
/**
|
672 |
672 |
@defgroup eps_io Postscript Exporting
|
673 |
673 |
@ingroup io_group
|
674 |
674 |
\brief General \c EPS drawer and graph exporter
|
675 |
675 |
|
676 |
676 |
This group contains general \c EPS drawing methods and special
|
677 |
677 |
graph exporting tools.
|
678 |
678 |
*/
|
679 |
679 |
|
680 |
680 |
/**
|
681 |
681 |
@defgroup dimacs_group DIMACS Format
|
682 |
682 |
@ingroup io_group
|
683 |
683 |
\brief Read and write files in DIMACS format
|
684 |
684 |
|
685 |
685 |
Tools to read a digraph from or write it to a file in DIMACS format data.
|
686 |
686 |
*/
|
687 |
687 |
|
688 |
688 |
/**
|
689 |
689 |
@defgroup nauty_group NAUTY Format
|
690 |
690 |
@ingroup io_group
|
691 |
691 |
\brief Read \e Nauty format
|
692 |
692 |
|
693 |
693 |
Tool to read graphs from \e Nauty format data.
|
694 |
694 |
*/
|
695 |
695 |
|
696 |
696 |
/**
|
697 |
697 |
@defgroup concept Concepts
|
698 |
698 |
\brief Skeleton classes and concept checking classes
|
699 |
699 |
|
700 |
700 |
This group contains the data/algorithm skeletons and concept checking
|
701 |
701 |
classes implemented in LEMON.
|
702 |
702 |
|
703 |
703 |
The purpose of the classes in this group is fourfold.
|
704 |
704 |
|
705 |
705 |
- These classes contain the documentations of the %concepts. In order
|
706 |
706 |
to avoid document multiplications, an implementation of a concept
|
707 |
707 |
simply refers to the corresponding concept class.
|
708 |
708 |
|
709 |
709 |
- These classes declare every functions, <tt>typedef</tt>s etc. an
|
710 |
710 |
implementation of the %concepts should provide, however completely
|
711 |
711 |
without implementations and real data structures behind the
|
712 |
712 |
interface. On the other hand they should provide nothing else. All
|
713 |
713 |
the algorithms working on a data structure meeting a certain concept
|
714 |
714 |
should compile with these classes. (Though it will not run properly,
|
715 |
715 |
of course.) In this way it is easily to check if an algorithm
|
716 |
716 |
doesn't use any extra feature of a certain implementation.
|
717 |
717 |
|
718 |
718 |
- The concept descriptor classes also provide a <em>checker class</em>
|
719 |
719 |
that makes it possible to check whether a certain implementation of a
|
720 |
720 |
concept indeed provides all the required features.
|
721 |
721 |
|
722 |
722 |
- Finally, They can serve as a skeleton of a new implementation of a concept.
|
723 |
723 |
*/
|
724 |
724 |
|
725 |
725 |
/**
|
726 |
726 |
@defgroup graph_concepts Graph Structure Concepts
|
727 |
727 |
@ingroup concept
|
728 |
728 |
\brief Skeleton and concept checking classes for graph structures
|
729 |
729 |
|
730 |
730 |
This group contains the skeletons and concept checking classes of
|
731 |
731 |
graph structures.
|
732 |
732 |
*/
|
733 |
733 |
|
734 |
734 |
/**
|
735 |
735 |
@defgroup map_concepts Map Concepts
|
736 |
736 |
@ingroup concept
|
737 |
737 |
\brief Skeleton and concept checking classes for maps
|
738 |
738 |
|
739 |
739 |
This group contains the skeletons and concept checking classes of maps.
|
740 |
740 |
*/
|
741 |
741 |
|
742 |
742 |
/**
|
743 |
743 |
@defgroup tools Standalone Utility Applications
|
744 |
744 |
|
745 |
745 |
Some utility applications are listed here.
|
746 |
746 |
|
747 |
747 |
The standard compilation procedure (<tt>./configure;make</tt>) will compile
|
748 |
748 |
them, as well.
|
749 |
749 |
*/
|
750 |
750 |
|
751 |
751 |
/**
|
752 |
752 |
\anchor demoprograms
|
753 |
753 |
|
754 |
754 |
@defgroup demos Demo Programs
|
755 |
755 |
|
756 |
756 |
Some demo programs are listed here. Their full source codes can be found in
|
757 |
757 |
the \c demo subdirectory of the source tree.
|
758 |
758 |
|
759 |
759 |
In order to compile them, use the <tt>make demo</tt> or the
|
760 |
760 |
<tt>make check</tt> commands.
|
761 |
761 |
*/
|
762 |
762 |
|
763 |
763 |
}
|