Changeset 844:c01a98ce01fd in lemon

Timestamp:

05/12/09 13:09:55 (15 years ago)

Author:

Alpar Juttner <alpar@…>

Branch:

1.1

Parents:

843:189760a7cdd0 (diff), 712:e652b6f9a29f (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Phase:

public

Message:

Merge

Files:

• doc/groups.dox (modified) (9 diffs)
• doc/groups.dox (modified) (5 diffs)
• lemon/bits/base_extender.h (deleted)

doc/groups.dox

@@ -227 +227 @@
 
 /**
-@defgroup matrices Matrices
-@ingroup datas
-\brief Two dimensional data storages implemented in LEMON.
-
-This group contains two dimensional data storages implemented in LEMON.
-*/
-
-/**
 @defgroup paths Path Structures
 @ingroup datas
@@ -284 +276 @@
 This group contains the algorithms for finding shortest paths in digraphs.
 
- - \ref Dijkstra algorithm for finding shortest paths from a source node
-   when all arc lengths are non-negative.
- - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
-   from a source node when arc lenghts can be either positive or negative,
-   but the digraph should not contain directed cycles with negative total
-   length.
- - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
-   for solving the \e all-pairs \e shortest \e paths \e problem when arc
-   lenghts can be either positive or negative, but the digraph should
-   not contain directed cycles with negative total length.
+ - \ref Dijkstra Dijkstra's algorithm for finding shortest paths from a 
+   source node when all arc lengths are non-negative.
  - \ref Suurballe A successive shortest path algorithm for finding
    arc-disjoint paths between two nodes having minimum total length.
@@ -318 +302 @@
 \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.
-
-In most cases the \ref Preflow "Preflow" algorithm provides the
-fastest method for computing a maximum flow. All implementations
-also provide functions to query the minimum cut, which is the dual
-problem of maximum flow.
+\ref Preflow implements the preflow push-relabel algorithm of Goldberg and
+Tarjan for solving this problem. It also provides functions to query the
+minimum cut, which is the dual problem of maximum flow.
+
 
 \ref Circulation is a preflow push-relabel algorithm implemented directly 
@@ -345 +323 @@
 solution see \ref min_cost_flow "Minimum Cost Flow Problem".
 
-LEMON contains several algorithms for this problem.
- - \ref NetworkSimplex Primal Network Simplex algorithm with various
-   pivot strategies.
- - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
-   cost scaling.
- - \ref CapacityScaling Successive Shortest %Path algorithm with optional
-   capacity scaling.
- - \ref CancelAndTighten The Cancel and Tighten algorithm.
- - \ref CycleCanceling Cycle-Canceling algorithms.
-
-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).
+\ref NetworkSimplex is an efficient implementation of the primal Network
+Simplex algorithm for finding minimum cost flows. It also provides dual
+solution (node potentials), if an optimal flow is found.
 */
 
@@ -382 +349 @@
 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   in directed graphs.
-- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
-  calculating minimum cut in undirected graphs.
 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   all-pairs minimum cut in undirected graphs.
@@ -404 +369 @@
 
 /**
-@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 matching Matching Algorithms
 @ingroup algs
 \brief Algorithms for finding matchings in graphs and bipartite graphs.
 
-This group contains the algorithms for calculating
-matchings in graphs and bipartite graphs. The general matching problem is
-finding a subset of the edges for which each node has at most one incident
-edge.
+This group contains the algorithms for calculating matchings in graphs.
+The general matching problem is 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
-easier than in general graphs. The goal of the matching optimization
+graphs. The goal of the matching optimization
 can be finding maximum cardinality, maximum weight or minimum cost
 matching. The search can be constrained to find perfect or
@@ -433 +384 @@
 
 The matching algorithms implemented in LEMON:
-- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
-  for calculating maximum cardinality matching in bipartite graphs.
-- \ref PrBipartiteMatching Push-relabel algorithm
-  for calculating maximum cardinality matching in bipartite graphs.
-- \ref MaxWeightedBipartiteMatching
-  Successive shortest path algorithm for calculating maximum weighted
-  matching and maximum weighted bipartite matching in bipartite graphs.
-- \ref MinCostMaxBipartiteMatching
-  Successive shortest path algorithm for calculating minimum cost maximum
-  matching in bipartite graphs.
 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   maximum cardinality matching in general graphs.
@@ -474 +415 @@
 
 /**
-@defgroup approx Approximation Algorithms
-@ingroup algs
-\brief Approximation algorithms.
-
-This group contains the approximation and heuristic algorithms
-implemented in LEMON.
-*/
-
-/**
 @defgroup gen_opt_group General Optimization Tools
 \brief This group contains some general optimization frameworks
@@ -499 +431 @@
 various LP solvers could be used in the same manner with this
 interface.
-*/
-
-/**
-@defgroup lp_utils Tools for Lp and Mip Solvers
-@ingroup lp_group
-\brief Helper tools to the Lp and Mip solvers.
-
-This group adds some helper tools to general optimization framework
-implemented in LEMON.
-*/
-
-/**
-@defgroup metah Metaheuristics
-@ingroup gen_opt_group
-\brief Metaheuristics for LEMON library.
-
-This group contains some metaheuristic optimization tools.
 */
 

doc/groups.dox

@@ -139 +139 @@
 
 /**
-@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
-@ingroup graphs
-\brief Graph types between real graphs and graph adaptors.
-
-This group contains 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
@@ -316 +306 @@
 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,
@@ -323 +314 @@
 
 /**
-@defgroup min_cost_flow Minimum Cost Flow Algorithms
+@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
 @ingroup algs
 
@@ -329 +320 @@
 
 This group contains the algorithms for finding minimum cost flows and
-circulations.
-
-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 (lower and upper bounds)
-and arc costs.
-Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
-\f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
-upper bounds for the flow values on the arcs, for which
-\f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
-\f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
-on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
-signed supply values of the nodes.
-If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
-supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
-\f$-sup(u)\f$ demand.
-A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
-of the following optimization problem.
-
-\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
-\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
-    sup(u) \quad \forall u\in V \f]
-\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
-
-The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
-zero or negative in order to have a feasible solution (since the sum
-of the expressions on the left-hand side of the inequalities is zero).
-It means that the total demand must be greater or equal to the total
-supply and all the supplies have to be carried out from the supply nodes,
-but there could be demands that are not satisfied.
-If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
-constraints have to be satisfied with equality, i.e. all demands
-have to be satisfied and all supplies have to be used.
-
-If you need the opposite inequalities in the supply/demand constraints
-(i.e. the total demand is less than the total supply and all the demands
-have to be satisfied while there could be supplies that are not used),
-then you could easily transform the problem to the above form by reversing
-the direction of the arcs and taking the negative of the supply values
-(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
-However \ref NetworkSimplex algorithm also supports this form directly
-for the sake of convenience.
-
-A feasible solution for this problem can be found using \ref Circulation.
-
-Note that the above formulation is actually more general than the usual
-definition of the minimum cost flow problem, in which strict equalities
-are required in the supply/demand contraints, i.e.
-
-\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
-    sup(u) \quad \forall u\in V. \f]
-
-However if the sum of the supply values is zero, then these two problems
-are equivalent. So if you need the equality form, you have to ensure this
-additional contraint for the algorithms.
-
-The dual solution of the minimum cost flow problem is represented by node 
-potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
-An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
-is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
-node potentials the following \e complementary \e slackness optimality
-conditions hold.
-
- - For all \f$uv\in A\f$ arcs:
-   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
-   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
-   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
- - For all \f$u\in V\f$ nodes:
-   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
-     then \f$\pi(u)=0\f$.
- 
-Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
-\f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
-\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
+circulations. For more information about this problem and its dual
+solution see \ref min_cost_flow "Minimum Cost Flow Problem".
 
 \ref NetworkSimplex is an efficient implementation of the primal Network
@@ -480 +399 @@
 @defgroup spantree Minimum Spanning Tree Algorithms
 @ingroup algs
-\brief Algorithms for finding a minimum cost spanning tree in a graph.
-
-This group contains the algorithms for finding a minimum cost spanning
-tree in a graph.
+\brief Algorithms for finding minimum cost spanning trees and arborescences.
+
+This group contains the algorithms for finding minimum cost spanning
+trees and arborescences.
 */