The Maximum TSP

Abstract

Introduction The Maximum Traveling Salesman Problem (MAX TSP), also known informally as the "taxicab ripoff problem", is stated as follows: Given an n \Theta n real matrix c = (c ij ), called a weight matrix, find a hamiltonian cycle i 1 7! i 2 7! : : : 7! i n 7! i 1 , for which the maximum value of c i 1 i 2 + c i 2 i 3 + : : : + c i n\Gamma1 i n + c i n i 1 is attained. Here (i 1 ; : : : ; i n ) is a permutation of the set f1; : : : ; ng. Of course, in this general setting, the Maximum Traveling Salesman Problem is equivalent to the Minimum Traveling Salesman Problem, Partially supported by NSF Grant DMS 9734138 since the maximum weight hamiltonian cycle with the weight matrix c corresponds to the minimum weight hamiltonian cycle with the weight matrix \Gammac. What makes the MAX TSP special is that there are some interesting and natural special cases of weights c ij , not preserved by the sign reversal, where much more can be said about the problem than in the general case. Be