The maximum traveling salesman problem on banded matrices

David Blokh, Eugene Levner

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the Maximum Traveling Salesman Problem on banded distance matrices. A (p, q)-banded matrix has all its non-zero elements contained within a band consisting of p diagonals above the principal diagonal and q diagonals below it. We investigate the properties of the problem and prove that the number K of different permutations which can be optimal solutions for different instances of the problem, is exponential in n where n is the problem size (= the number of cities). For the Maximum-TSP on the (2, 0)-banded matrices, K=O(λn) where 1.7548 <λ< 1.7549, whereas on the (1, 1)-banded matrices K=O(λn) where 1.6180 <λ< 1.6181. Using recursive equations, we derive a linear-time algorithm that exactly solves the Maximum-TSP on the (2, 0)-banded distance matrices.

Original languageEnglish
Pages (from-to)809-819
Number of pages11
JournalInternational Journal of Foundations of Computer Science
Volume12
Issue number6
DOIs
StatePublished - 2001
Externally publishedYes

Keywords

  • Banded matrices
  • Difference equations
  • Maxium traveling salesman problem
  • Polynomial algorithm

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