Synchronized Traveling Salesman Problem

TL;DR

This paper introduces the synchronized traveling salesman problem where multiple agents must tour a graph without crashing, establishing bounds on the number of agents and time horizon for specific graph classes.

Contribution

It formalizes the synchronized TSP, relates it to evacuation and dynamic flow problems, and provides bounds for agencies on trees and 3-connected 3-regular graphs.

Findings

Established upper and lower bounds for agencies on trees.

Established bounds for agencies on 3-connected 3-regular graphs.

Related the synchronized TSP to evacuation and dynamic flow problems.

Abstract

We consider a variation of the well-known traveling salesman problem in which there are multiple agents who all have to tour the whole set of nodes of the same graph, while obeying node- and edge-capacity constraints require that agents must not "crash". We consider the simplest model in which the input is an undirected graph with all capacities equal to one. A solution to the synchronized traveling salesman problem is called an "agency". Our model puts the synchronized traveling salesman problem in a similar relation with the traveling salesman problem as the so-called evacuation problem, or the well-known dynamic flow (flow-over-time) problem is in relation with the minimum cost flow problem. We measure the strength of an agency in terms of number of agents which should be as large as possible, and the time horizon which should be as small as possible. Beside some elementary discussion of the notions introduced, we establish several upper and lower bounds for the strength of an agency under the assumption that the input graph is a tree, or a 3-connected 3-regular graph.