A Reusable Framework for Robust Approximation Algorithms in the Interval Uncertainty Model

2026-09-10

AI Summary

本文针对区间不确定性下的鲁棒优化问题，通过改进局部搜索算法，提出了适用于加权k-集合覆盖问题的首个鲁棒近似算法。

Abstract

Robust optimization under interval uncertainty aims to compute solutions that perform well on a range of scenarios that are described by interval-constrained costs. In this paper, we revisit a framework introduced by Ganesh, Maggs and Panigrahi in 2020 to study the robust optimization of NP-hard problems under interval uncertainty. We start by generalizing a result in the $\ell=0$ case, which transforms a category of approximation algorithms into a robust approximation algorithm. Furthermore, in the general case, we provide a theorem that turns any local search-based approximation algorithm into a robust approximation algorithm under three newly formalized conditions over the moves of the local search algorithm. We then use this result to present the first robust approximation algorithm for Weighted $k$-Set Cover, the third NP-hard problem known to admit a robust approximation, and the first since the publication of Ganesh, Maggs and Panigrahi's paper.

Problem

• robust optimization
• interval uncertainty
• approximation algorithms
• NP-hard problems

Innovation

• robust approximation algorithm
• interval uncertainty model
• local search-based approximation
• weighted k-set cover