2026-07-21T14:13:51Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:3859 2024-03-06T10:34:32Z ddc:004 open_access

Scheduling Resources for Executing a Partial Set of Jobs Chakaravarthy, Venkatesan T. Pal, Arindam Roy, Sambuddha Sabharwal, Yogish Approximation Algorithms Partial Covering Interval Graphs In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. We consider two versions of this problem. In the partial covering version, we are also given as input a number k, specifying the number of jobs that must be performed. The goal is to choose $k$ jobs and find a minimum cost set of resources to perform the chosen k jobs (at any point of time the capacity of the chosen set of resources should be sufficient to execute the jobs active at that time). We present an O(log n)-factor approximation algorithm for this problem. We also consider the prize collecting version, wherein every job also has a penalty associated with it. The feasible solution consists of a subset of the jobs, and a set of resources, to perform the chosen subset of jobs. The goal is to find a feasible solution that minimizes the sum of the costs of the selected resources and the penalties of the jobs that are not selected. We present a constant factor approximation algorithm for this problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Venkatesan T. Chakaravarthy and Arindam Pal and Sambuddha Roy and Yogish Sabharwal 2012 Is Part Of LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2012.199 urn:nbn:de:0030-drops-38598 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.199 eng https://creativecommons.org/licenses/by/3.0/legalcode