{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7246","name":"Scheduling Resources for Executing a Partial Set of Jobs","abstract":"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. \r\n\r\nIn 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. \r\n\r\nWe 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.","keywords":["Approximation Algorithms","Partial Covering","Interval Graphs"],"author":[{"@type":"Person","name":"Chakaravarthy, Venkatesan T.","givenName":"Venkatesan T.","familyName":"Chakaravarthy"},{"@type":"Person","name":"Pal, Arindam","givenName":"Arindam","familyName":"Pal"},{"@type":"Person","name":"Roy, Sambuddha","givenName":"Sambuddha","familyName":"Roy"},{"@type":"Person","name":"Sabharwal, Yogish","givenName":"Yogish","familyName":"Sabharwal"}],"position":19,"pageStart":199,"pageEnd":210,"dateCreated":"2012-12-14","datePublished":"2012-12-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chakaravarthy, Venkatesan T.","givenName":"Venkatesan T.","familyName":"Chakaravarthy"},{"@type":"Person","name":"Pal, Arindam","givenName":"Arindam","familyName":"Pal"},{"@type":"Person","name":"Roy, Sambuddha","givenName":"Sambuddha","familyName":"Roy"},{"@type":"Person","name":"Sabharwal, Yogish","givenName":"Yogish","familyName":"Sabharwal"}],"copyrightYear":"2012","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2012.199","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6221","volumeNumber":18,"name":"IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)","dateCreated":"2012-12-14","datePublished":"2012-12-14","editor":[{"@type":"Person","name":"D'Souza, Deepak","givenName":"Deepak","familyName":"D'Souza"},{"@type":"Person","name":"Radhakrishnan, Jaikumar","givenName":"Jaikumar","familyName":"Radhakrishnan"},{"@type":"Person","name":"Telikepalli, Kavitha","givenName":"Kavitha","familyName":"Telikepalli"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7246","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6221"}}}