Robust Algorithms for TSP and Steiner Tree

TL;DR

This paper develops robust algorithms with constant regret approximations for the NP-hard Traveling Salesman Problem and Steiner Tree problem, extending robust optimization techniques to complex combinatorial problems.

Contribution

It introduces the first robust polynomial-time algorithms with constant regret approximations for TSP and Steiner Tree, previously known only for simpler graph problems.

Findings

Achieved constant regret approximation algorithms for TSP and Steiner Tree.

Extended robust optimization techniques to NP-hard combinatorial problems.

Provided theoretical guarantees on the performance of the algorithms.

Abstract

Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret, defined as the maximum difference between the solution's cost and that of an optimal solution in hindsight once the input has been realized. For graph problems in P, such as shortest path and minimum spanning tree, robust polynomial-time algorithms that obtain a constant approximation on regret are known. In this paper, we study robust algorithms for minimizing regret in NP-hard graph optimization problems, and give constant approximations on regret for the classical traveling salesman and Steiner tree problems.