Online Rounding for Set Cover under Subset Arrivals
Jaros{\l}aw Byrka, Yongho Shin

TL;DR
This paper introduces an improved online rounding scheme for set cover problems under subset arrivals, achieving better approximation guarantees and extending to special cases like edge cover.
Contribution
It presents an O(log^2 s)-competitive rounding scheme for subset arrival models, improving previous bounds, and offers a 1.8-competitive scheme for edge cover.
Findings
Achieves O(log^2 s)-competitive ratio under subset arrival model.
Provides an improved approximation for multi-stage stochastic set cover.
Develops a 1.8-competitive scheme for edge cover.
Abstract
A rounding scheme for set cover has served as an important component in design of approximation algorithms for the problem, and there exists an H_s-approximate rounding scheme, where s denotes the maximum subset size, directly implying an approximation algorithm with the same approximation guarantee. A rounding scheme has also been considered under some online models, and in particular, under the element arrival model used as a crucial subroutine in algorithms for online set cover, an O(log s)-competitive rounding scheme is known [Buchbinder, Chen, and Naor, SODA 2014]. On the other hand, under a more general model, called the subset arrival model, only a simple O(log n)-competitive rounding scheme is known, where n denotes the number of elements in the ground set. In this paper, we present an O(log^2 s)-competitive rounding scheme under the subset arrival model, with one mild…
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Taxonomy
TopicsOptimization and Search Problems · Algorithms and Data Compression · Complexity and Algorithms in Graphs
