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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Bibliographic Details
Published in:Operations Research Forum Vol. 3; no. 1; p. 20
Main Author: Christofides, Nicos
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2022
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2662-2556
2662-2556
DOI:10.1007/s43069-021-00101-z