Preemptive and non-preemptive generalized min sum set cover

S. Im, M. Sviridenko, G.R.J. van der Zwaan

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

In the (non-preemptive) Generalized Min Sum Set Cover Problem, we are given n ground elements and a collection of sets S = {S-1, S-2,...,S-m} where each set S-i is an element of 2([n]) has a positive requirement k(S-i) that has to be fulfilled. We would like to order all elements to minimize the total (weighted) cover time of all sets. The cover time of a set S-i is defined as the first index j in the ordering such that the first j elements in the ordering contain k(S-i) elements in S-i. This problem was introduced by [1] with interesting motivations in web page ranking and broadcast scheduling. For this problem, constant approximations are known [2, 15].We study the version where preemption is allowed. The difference is that elements can be fractionally scheduled and a set S is covered in the moment when k(S) amount of elements in S are scheduled. We give a 2-approximation for this preemptive problem. Our linear programming and analysis are completely different from [2, 15]. We also show that any preemptive solution can be transformed into a non-preemptive one by losing a factor of 6.2 in the objective function. As a byproduct, we obtain an improved 12.4-approximation for the non-preemptive problem.
Original languageEnglish
Title of host publicationLeibniz International Proceedings in Informatics
EditorsC. Dürr, T. Wilke
Place of PublicationGermany
PublisherLeibniz-Zentrum für Informatik, Dagstuhl Publising Germany
Pages465-476
ISBN (Print)978-3-939897-35-4
DOIs
Publication statusPublished - 1 Jan 2012

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