Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem

An O( n 3 ) heuristic algorithm is described for solving d -city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cos...

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Vydáno v:Operations Research Forum Ročník 3; číslo 1; s. 20
Hlavní autor: Christofides, Nicos
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.03.2022
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Business and Management
Graph coloring
Graph theory
Heuristic
Heuristic methods
Math Applications in Computer Science
Mathematical and Computational Engineering
Minimum cost
Operations Research/Decision Theory
Optimization
Original Research
Polynomials
Traveling salesman problem
ISSN:2662-2556, 2662-2556
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Abstract An O( n 3 ) heuristic algorithm is described for solving d -city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G . A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.
AbstractList An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G. A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.
An O( n 3 ) heuristic algorithm is described for solving d -city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G . A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.
ArticleNumber 20
Author Christofides, Nicos
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Cites_doi 10.1137/0119070
10.1145/321921.321926
10.1137/0203025
10.1109/SWAT.1974.4
10.1287/mnsc.17.5.259
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Snippet An O( n 3 ) heuristic algorithm is described for solving d -city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition....
An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The...
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SubjectTerms Algorithms
Applications of Mathematics
Business and Management
Graph coloring
Graph theory
Heuristic
Heuristic methods
Math Applications in Computer Science
Mathematical and Computational Engineering
Minimum cost
Operations Research/Decision Theory
Optimization
Original Research
Polynomials
Traveling salesman problem
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