dir_min_cycle_basis.h File Reference


Detailed Description

Algorithms for directed MCB.

Given an directed graph $G(V,E)$ and a positive 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 vector in $Q^m$ indexed on the edge set, and operations between cycles is performed in $Q$. 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.

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

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

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::spvecfp

#include <LEDA/graph.h>
#include <LEDA/array.h>
#include <LEDA/edge_array.h>
#include <LEDA/list.h>
#include <LEDA/integer.h>
#include <LEDA/p_queue.h>
#include <LEDA/random_source.h>
#include <LEDA/sortseq.h>
#include <LEDA/tuple.h>
#include <LEP/mcb/edge_num.h>
#include <LEP/mcb/fp.h>
#include <LEP/mcb/arithm.h>

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Namespaces

namespace  mcb

Functions

template<class W>
mcb::DIR_MIN_CYCLE_BASIS (const graph &g, const edge_array< W > &len, array< spvecfp > &mcb, array< spvecfp > &proof, const edge_num &enumb, double error=0.375)
 Compute a minimum cycle basis of a weighted directed graph.
template<class W>
mcb::DIR_MIN_CYCLE_BASIS (const graph &g, const edge_array< W > &len, array< array< etype > > &mcb, const edge_num &enumb, double error=0.375)
 Compute a minimum cycle basis of a weighted directed graph.
template<class W>
mcb::DIR_MIN_CYCLE_BASIS (const graph &g, const edge_array< W > &len, array< list< edge > > &mcb, double error=0.375)
 Compute a minimum cycle basis of a weighted directed graph.


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