TY - JOUR

T1 - The maximum Travelling Salesman Problem on symmetric Demidenko matrices

AU - Deineko, V.G.

AU - Woeginger, G.J.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

U2 - 10.1016/S0166-218X(99)00148-1

DO - 10.1016/S0166-218X(99)00148-1

M3 - Article

VL - 99

SP - 413

EP - 425

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -