The Maximum Travelling Salesman Problem on symmetric Demidenko matrices

doi:10.1016/S0166-218X(99)00148-1

Discrete Applied Mathematics

Volume 99, Issues 1–3, 1 February 2000, Pages 413-425

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Abstract

It is well-known that the Travelling Salesman Problem (TSP) is solvable in polynomial time, if the distance matrix fulfills the so-called Demidenko conditions. This paper investigates the closely related Maximum Travelling Salesman Problem (MaxTSP) on symmetric Demidenko matrices. Somewhat surprisingly, we show that — in strong contrast to the minimization problem — the maximization problem is NP-hard to solve. Moreover, we identify several special cases that are solvable in polynomial time. These special cases contain and generalize several predecessor results by Quintas and Supnick and by Kalmanson.

MSC

primary: 90C27

Keywords

Travelling salesman problem

Demidenko condition

Kalmanson condition

Supnick condition

Combinatorial optimization

Computational complexity

Polynomial algorithm

Cited by (0)

¹: On leave from Department of Applied Mathematics, Dnepropetrovsk University, Gagarin Av. 72, 320625 Dnepropetrovsk, Ukraine.

²: Supported by the START program Y43-MAT of the Austrian Ministry of Science.