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The Travelling Salesman Problem in symmetric circulant matrices with two stripes

Published online by Cambridge University Press:  01 February 2008

IVAN GERACE  and
FEDERICO GRECO
IVAN GERACE
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, I-06123 Perugia, Italy Email: [email protected], [email protected]
FEDERICO GRECO
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, I-06123 Perugia, Italy Email: [email protected], [email protected]
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Abstract

The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 165 - 175
Copyright
Copyright © Cambridge University Press2008

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