Complexity indices for the traveling salesman problem continued

Abstract

We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs G with distances between cities as edge weights. A complexity index is an invariant of an instance I by which we predict the execution time of an exact TSP algorithm for I. In the paper [5] we have considered some short edge subgraphs of G and defined several new invariants related to their connected components. Extensive computational experiments with instances on 50 vertices with the uniform distribution of integer edge weights in the interval [1,100] show that there exists correlation between the sequences of selected invariants and the sequence of execution times of the well-known TSP Solver Concorde. In this paper we extend these considerations for instances up to 100 vertices.