ChristofidesTsp< CM > Class Template Reference

Detailed Description

template<typename CM>
class lemon::ChristofidesTsp< CM >

ChristofidesTsp implements Christofides' heuristic for solving symmetric TSP.

This a well-known approximation method for the TSP problem with metric cost function. It has a guaranteed approximation factor of 3/2 (i.e. it finds a tour whose total cost is at most 3/2 of the optimum), but it usually provides better solutions in practice. This implementation runs in O(n³log(n)) time.

The algorithm starts with a minimum cost spanning tree and finds a minimum cost perfect matching in the subgraph induced by the nodes that have odd degree in the spanning tree. Finally, it constructs the tour from the Euler traversal of the union of the spanning tree and the matching. During this last step, the algorithm simply skips the visited nodes (i.e. creates shortcuts) assuming that the triangle inequality holds for the cost function.

Template Parameters

CM	Type of the cost map.

Warning

CM::Value must be a signed number type.

#include <lemon/christofides_tsp.h>

Public Types
typedef CM	CostMap
	Type of the cost map.
typedef CM::Value	Cost
	Type of the edge costs.

Public Member Functions
	ChristofidesTsp (const FullGraph &gr, const CostMap &cost)
	Constructor.
Execution Control
Cost	run ()
	Runs the algorithm.
Query Functions
Cost	tourCost () const
	The total cost of the found tour.
const std::vector< Node > &	tourNodes () const
	Returns a const reference to the node sequence of the found tour.
template<typename Iterator >
void	tourNodes (Iterator out) const
	Gives back the node sequence of the found tour.
template<typename Path >
void	tour (Path &path) const
	Gives back the found tour as a path.

Constructor & Destructor Documentation

ChristofidesTsp ( const FullGraph &  gr, const CostMap &  cost  )

inline

Constructor.

Parameters

gr	The full graph the algorithm runs on.
cost	The cost map.

Member Function Documentation

Cost run ( )

inline

This function runs the algorithm.

Returns

The total cost of the found tour.

Cost tourCost ( ) const

inline

This function returns the total cost of the found tour.

Precondition

run() must be called before using this function.

const std::vector<Node>& tourNodes ( ) const

inline

This function returns a const reference to a vector that stores the node sequence of the found tour.

Precondition

run() must be called before using this function.

void tourNodes ( Iterator  out ) const

inline

This function copies the node sequence of the found tour into an STL container through the given output iterator. The value_type of the container must be FullGraph::Node. For example,

std::vector<FullGraph::Node> nodes(countNodes(graph));
tsp.tourNodes(nodes.begin());

or

std::list<FullGraph::Node> nodes;
tsp.tourNodes(std::back_inserter(nodes));

Precondition

run() must be called before using this function.

void tour ( Path &  path ) const

inline

This function copies the found tour as a list of arcs/edges into the given path structure.

Precondition

run() must be called before using this function.