## Class TwoApproxMetricTSP<V,​E>

• java.lang.Object
• org.jgrapht.alg.tour.TwoApproxMetricTSP<V,​E>
• Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
HamiltonianCycleAlgorithm<V,​E>

public class TwoApproxMetricTSP<V,​E>
extends java.lang.Object
implements HamiltonianCycleAlgorithm<V,​E>
A 2-approximation algorithm for the metric TSP problem.

The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?". In the metric TSP, the intercity distances satisfy the triangle inequality.

This is an implementation of the folklore algorithm which returns a depth-first ordering of the minimum spanning tree. The algorithm is a 2-approximation assuming that the instance satisfies the triangle inequality. The implementation requires the input graph to be undirected and complete. The running time is $O(|V|^2 \log |V|)$.

See wikipedia for more details.

Author:
Dimitrios Michail
• ### Constructor Summary

Constructors
Constructor Description
TwoApproxMetricTSP()
Construct a new instance
• ### Method Summary

All Methods
Modifier and Type Method Description
GraphPath<V,​E> getTour​(Graph<V,​E> graph)
Computes a 2-approximate tour.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### TwoApproxMetricTSP

public TwoApproxMetricTSP()
Construct a new instance
• ### Method Detail

• #### getTour

public GraphPath<V,​E> getTour​(Graph<V,​E> graph)
Computes a 2-approximate tour.
Specified by:
getTour in interface HamiltonianCycleAlgorithm<V,​E>
Parameters:
graph - the input graph
Returns:
a tour
Throws:
java.lang.IllegalArgumentException - if the graph is not undirected
java.lang.IllegalArgumentException - if the graph is not complete
java.lang.IllegalArgumentException - if the graph contains no vertices