On the Recoverable Traveling Salesman Problem

TL;DR

This paper introduces the Recoverable Traveling Salesman Problem, proposing approximation algorithms that find two tours with minimal total distance while maintaining a minimum intersection size, extending classic methods to a new robust optimization context.

Contribution

It develops a 4-approximation algorithm for the Recoverable TSP and a 2-approximation for constant intersection sizes, advancing the understanding of robust tour planning.

Findings

A 4-approximation algorithm for Recoverable TSP.

A 2-approximation guarantee for constant intersection sizes.

Implications for recoverable robust optimization are discussed.

Abstract

In this paper we consider the Recoverable Traveling Salesman Problem (TSP). Here the task is to find two tours simultaneously, such that the intersection between the tours is at least a given minimum size, while the sum of travel distances with respect to two different distance metrics is minimized. Building upon the classic double-tree method, we derive a 4-approximation algorithm for the RecoverableTSP. We also show that if the required size of the intersection between the tours is constant, a 2-approximation guarantee can be achieved, even if more than two tours need to be constructed. We discuss consequences for approximability results in the more general area of recoverable robust optimization.