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

Abstract

An O(n sup 3) heuristic algorithm is described for solving n-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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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1976
Accession Number
ADA025602

Entities

People

  • Nicos Christofides

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Commerce
  • Computations
  • Cooperation
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Pennsylvania
  • Polynomials
  • Schools
  • Sequences
  • Students
  • Training
  • Triangles
  • Universities

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research