{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1849","name":"Approximating min-max k-clustering","abstract":"We consider the\r\nproblems\r\n of set partitioning into $k$ clusters with minimum of the maximum cost of a cluster. The cost function is given by an oracle, and we assume that it satisfies some natural structural constraints. That is, we assume that the cost function is monotone, the cost of a singleton is zero, and we assume that for all $S cap S' \r\neq emptyset$ the following holds\r\n $c(S) + c(S') geq c(S cup S')$. For this problem we present\r\na $(2k-1)$-approximation algorithm for $kgeq 3$, a\r\n2-approximation algorithm for $k=2$, and we also show a lower\r\nbound of $k$ on the performance guarantee of any\r\n polynomial-time algorithm.\r\n\r\nWe then consider special cases of this problem arising in vehicle routing problems, and present improved results.","keywords":"Approximation algorithms","author":{"@type":"Person","name":"Levin, Asaf","givenName":"Asaf","familyName":"Levin"},"position":4,"pageStart":1,"pageEnd":5,"dateCreated":"2007-11-26","datePublished":"2007-11-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Levin, Asaf","givenName":"Asaf","familyName":"Levin"},"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07261.4","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":"#article1849","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"}}}