{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1855","name":"Maximizing the Minimum Load for Selfisch Agents","abstract":"We consider the problem of maximizing the minimum load for\r\nmachines that are controlled by selfish agents, who are only\r\ninterested in maximizing their own profit. Unlike the classical\r\nload balancing problem, this problem \r\nhas not been considered for selfish agents until now.\r\n\r\nFor a constant number of machines, $m$, we show a\r\nmonotone polynomial time approximation scheme (PTAS) with running\r\ntime that is linear in the number of jobs. It uses a new\r\ntechnique for reducing the number of jobs while remaining close\r\nto the optimal solution. We also present an FPTAS for the classical\r\nmachine covering problem, i.e., where no selfish agents are involved\r\n(the previous best result for this case was a PTAS)\r\nand use this to give a monotone FPTAS.\r\n\r\nAdditionally, we give a monotone approximation algorithm with\r\napproximation ratio $min(m,(2+eps)s_1\/s_m)$ where $eps>0$ can\r\nbe chosen arbitrarily small and $s_i$ is the (real) speed of\r\nmachine $i$. Finally we give improved results for two machines.","keywords":["Scheduling","algorithmic mechanism design","maximizing minimum load"],"author":[{"@type":"Person","name":"Epstein, Leah","givenName":"Leah","familyName":"Epstein"},{"@type":"Person","name":"van Stee, Rob","givenName":"Rob","familyName":"van Stee"}],"position":10,"pageStart":1,"pageEnd":0,"dateCreated":"2007-11-26","datePublished":"2007-11-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Epstein, Leah","givenName":"Leah","familyName":"Epstein"},{"@type":"Person","name":"van Stee, Rob","givenName":"Rob","familyName":"van Stee"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07261.10","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume658","volumeNumber":7261,"name":"Dagstuhl Seminar Proceedings, Volume 7261","dateCreated":"2007-11-26","datePublished":"2007-11-26","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1855","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume658"}}}