Analysis of the Traveling Salesman Problem with Flexible Colors

Abstract

This paper analizes a new variant of the Traveling Salesman Problem (TSP) in which nodes belong to various color classes and each color class must be visited as an entity. We show that the problem is APX-hard and provide exact solutions for special cases and a two-phase heuristic for the general case. Lastly, we analyze the worst case and asymptotic performanc of the heuristic.