An Experimental Evaluation of the Best-of-Many Christofides’ Algorithm for the Traveling Salesman Problem

Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant of the well-known Christofides’ algorithm for the TSP, called the Best-of-Many Christofides’ algorithm . The algorithm involves sampling a spanning tree from the solution to the standard LP re...

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Vydáno v:Algorithmica Ročník 78; číslo 4; s. 1109 - 1130
Hlavní autoři: Genova, Kyle, Williamson, David P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2017
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Computing costs
Cost engineering
Data Structures and Information Theory
Graph theory
Mathematics of Computing
Maximum entropy
Sampling
Theory of Computation
Traveling salesman problem
Christofides’ algorithm
Traveling salesman problem
Approximation algorithms
Maximum entropy
ISSN:0178-4617, 1432-0541
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Shrnutí:Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant of the well-known Christofides’ algorithm for the TSP, called the Best-of-Many Christofides’ algorithm . The algorithm involves sampling a spanning tree from the solution to the standard LP relaxation of the TSP, subject to the condition that each edge is sampled with probability at most its value in the LP relaxation. One then runs Christofides’ algorithm on the tree by computing a minimum-cost matching on the odd-degree vertices in the tree, and shortcutting a traversal of the resulting Eulerian graph to a tour. In this paper we perform an experimental evaluation of the Best-of-Many Christofides’ algorithm to see if there are empirical reasons to believe its performance is better than that of Christofides’ algorithm. Furthermore, several different sampling schemes have been proposed; we implement several different schemes to determine which ones might be the most promising for obtaining improved performance guarantees over that of Christofides’ algorithm. In our experiments, all of the implemented methods perform significantly better than Christofides’ algorithm; an algorithm that samples from a maximum entropy distribution over spanning trees seems to be particularly good, though there are others that perform almost as well.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-017-0293-5