min_cycle_basis.h File Reference


Detailed Description

Algorithms for undirected MCB.

Given an undirected graph $G(V,E)$ and a non-negative length function on the edges $w: E \mapsto \mathcal{R}_{\ge 0}$, a minimum cycle basis is a set of cycles which can generate the cycle space and at the same time has minimum total length.

Each cycle of the graph is assumed to be a 0-1 vector indexed on the edge set, and operations between cycles is performed in GF(2). The length of a cycle basis is the sum of the length of its cycles and the length of a cycle is the sum of the length of its edges.

The solution of a minimum cycle basis problem can be in the following three forms.

Most functions of this section are templates functions. The template parameter W can be instantiated with any number type. Attention must be paid in order to avoid overflow of values.

The whole package is protected using a namespace called "mcb", and therefore using anything requires mcb::xx or the using namespace mcb directive.

See also:
mcb::edge_num mcb::spvecgf2

#include <LEDA/graph.h>
#include <LEDA/d_int_set.h>
#include <LEDA/edge_array.h>
#include <LEDA/node_array.h>
#include <LEDA/array.h>
#include <LEDA/list.h>
#include <LEDA/sortseq.h>
#include <LEDA/shortest_path.h>
#include <LEDA/templates/shortest_path.t>
#include <LEDA/tuple.h>
#include <LEP/mcb/SIGNED_GRAPH.h>

Include dependency graph for min_cycle_basis.h:

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Go to the source code of this file.

Namespaces

namespace  mcb

Functions

int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< leda::d_int_set > &mcb, leda::array< leda::d_int_set > &proof, const mcb::edge_num &enumb)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< leda::d_int_set > &mcb, const edge_num &enumb)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< mcb::spvecgf2 > &mcb, leda::array< mcb::spvecgf2 > &proof, const edge_num &enumb)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< mcb::spvecgf2 > &mcb, const edge_num &enumb)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< leda::list< leda::edge > > &mcb, leda::array< leda::list< leda::edge > > &proof)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_DEPINA (const leda::graph &g, leda::array< leda::list< leda::edge > > &mcb)
 Compute a MCB of an undirected unweighted graph using de Pina's algorithm.
int mcb::MIN_CYCLE_BASIS_HYBRID (const leda::graph &g, leda::array< leda::d_int_set > &mcb, leda::array< leda::d_int_set > &proof, const edge_num &enumb)
int mcb::MIN_CYCLE_BASIS_HYBRID (const leda::graph &g, leda::array< leda::d_int_set > &mcb, const edge_num &enumb)
int mcb::MIN_CYCLE_BASIS_HYBRID (const leda::graph &g, leda::array< leda::list< leda::edge > > &mcb, leda::array< leda::list< leda::edge > > &proof)
int mcb::MIN_CYCLE_BASIS_HYBRID (const leda::graph &g, leda::array< leda::list< leda::edge > > &mcb)
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< spvecgf2 > &mcb, array< spvecgf2 > &proof, const edge_num &enumb)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< d_int_set > &mcb, array< d_int_set > &proof, const edge_num &enumb)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< d_int_set > &mcb, const edge_num &enumb)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< spvecgf2 > &mcb, const edge_num &enumb)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< list< edge > > &mcb)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_DEPINA (const graph &g, const edge_array< W > &len, array< list< edge > > &mcb, array< list< edge > > &proof)
 Compute a MCB of an undirected weighted graph using de Pina's algorithm.
template<class W>
mcb::MIN_CYCLE_BASIS_HYBRID (const graph &g, const edge_array< W > &len, array< d_int_set > &mcb, array< d_int_set > &proof, const edge_num &enumb)
template<class W>
mcb::MIN_CYCLE_BASIS_HYBRID (const graph &g, const edge_array< W > &len, array< d_int_set > &mcb, const edge_num &enumb)
template<class W>
mcb::MIN_CYCLE_BASIS_HYBRID (const graph &g, const edge_array< W > &len, array< list< edge > > &mcb, array< list< edge > > &proof)
template<class W>
mcb::MIN_CYCLE_BASIS_HYBRID (const graph &g, const edge_array< W > &len, array< list< edge > > &mcb)


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