Traveling Salesmen in the Presence of Competition
Sandor P. Fekete, Rudolf Fleischer, Aviezri Fraenkel, and Matthias, Schmitt

TL;DR
This paper introduces the Competing Salesmen Problem, a two-player competitive variant of the Traveling Salesman Problem, analyzing its computational complexity and strategic properties on various graph structures.
Contribution
It formalizes the CSP, proves its PSPACE-completeness, and explores strategic outcomes and optimal strategies on bipartite graphs and trees.
Findings
CSP is PSPACE-complete even on bipartite graphs.
Starting player can lose even from the same vertex as the opponent.
On trees, the second player can avoid losing more than one customer.
Abstract
We propose the ``Competing Salesmen Problem'' (CSP), a 2-player competitive version of the classical Traveling Salesman Problem. This problem arises when considering two competing salesmen instead of just one. The concern for a shortest tour is replaced by the necessity to reach any of the customers before the opponent does. In particular, we consider the situation where players take turns, moving along one edge at a time within a graph G=(V,E). The set of customers is given by a subset V_C V of the vertices. At any given time, both players know of their opponent's position. A player wins if he is able to reach a majority of the vertices in V_C before the opponent does. We prove that the CSP is PSPACE-complete, even if the graph is bipartite, and both players start at distance 2 from each other. We show that the starting player may lose the game, even if both players start from the same…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOrganizational Management and Leadership · Consumer Market Behavior and Pricing
