An approximation algorithm with performance guarantees for the maximum traveling salesman problem on special matrices

David Blokh, Eugene Levner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we investigate the maximum traveling salesman problem (Max-TSP) on quasi-banded matrices. A matrix is quasi-banded with multiplier α if all its elements contained within a band of several diagonals above and below the principal diagonal are non-zero, and any element in the band is at least α times larger than the maximal element outside the band. We investigate the properties of the Max-TSP on the quasi-banded matrices, prove that it is strongly NP-hard and derive a linear-time approximation algorithm with a guaranteed performance.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalDiscrete Applied Mathematics
Volume119
Issue number1-2
DOIs
StatePublished - 15 Jun 2002
Externally publishedYes

Bibliographical note

Funding Information:
This research was supported in part by INTAS Grant no. 96-0812 and Grant no. 8951-2-98 from the Ministry of Science of Israel. Valuable comments and criticisms from two anonymous referees are gratefully acknowledged.

Keywords

  • Approximation algorithms with performance guarantees
  • Banded matrices
  • Maximum traveling salesman problem
  • Polynomial algorithm

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