{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article12311","name":"Faster Approximation Algorithms for Computing Shortest Cycles on Weighted Graphs","abstract":"Given an n-vertex m-edge graph G with non-negative edge-weights, a shortest cycle of G is one minimizing the sum of the weights on its edges. The girth of G is the weight of such a shortest cycle. We obtain several new approximation algorithms for computing the girth of weighted graphs: \r\n- For any graph G with polynomially bounded integer weights, we present a deterministic algorithm that computes, in O~(n^{5\/3}+m)-time, a cycle of weight at most twice the girth of G. This matches both the approximation factor and - almost - the running time of the best known subquadratic-time approximation algorithm for the girth of unweighted graphs. \r\n- Then, we turn our algorithm into a deterministic (2+epsilon)-approximation for graphs with arbitrary non-negative edge-weights, at the price of a slightly worse running-time in O~(n^{5\/3}polylog(1\/epsilon)+m). For that, we introduce a generic method in order to obtain a polynomial-factor approximation of the girth in subquadratic time, that may be of independent interest. \r\n- Finally, if we assume that the adjacency lists are sorted then we can get rid off the dependency in the number m of edges. Namely, we can transform our algorithms into an O~(n^{5\/3})-time randomized 4-approximation for graphs with non-negative edge-weights. This can be derandomized, thereby leading to an O~(n^{5\/3})-time deterministic 4-approximation for graphs with polynomially bounded integer weights, and an O~(n^{5\/3}polylog(1\/epsilon))-time deterministic (4+epsilon)-approximation for graphs with non-negative edge-weights. \r\n To the best of our knowledge, these are the first known subquadratic-time approximation algorithms for computing the girth of weighted graphs.","keywords":["girth","weighted graphs","approximation algorithms"],"author":{"@type":"Person","name":"Ducoffe, Guillaume","givenName":"Guillaume","familyName":"Ducoffe","email":"mailto:guillaume.ducoffe@ici.ro","affiliation":"National Institute for Research and Development in Informatics, Romania"},"position":49,"pageStart":"49:1","pageEnd":"49:13","dateCreated":"2019-07-04","datePublished":"2019-07-04","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Ducoffe, Guillaume","givenName":"Guillaume","familyName":"Ducoffe","email":"mailto:guillaume.ducoffe@ici.ro","affiliation":"National Institute for Research and Development in Informatics, Romania"},"copyrightYear":"2019","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2019.49","funding":"This work was supported by a grant of Romanian Ministry of Research and Innovation CCCDI-UEFISCDI. project no. 17PCCDI\/2018.","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/arxiv.org\/abs\/1704.02178","http:\/\/arxiv.org\/abs\/1810.10229"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6335","volumeNumber":132,"name":"46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)","dateCreated":"2019-07-04","datePublished":"2019-07-04","editor":[{"@type":"Person","name":"Baier, Christel","givenName":"Christel","familyName":"Baier","email":"mailto:christel.baier@tu-dresden.de","affiliation":"TU Dresden, Germany"},{"@type":"Person","name":"Chatzigiannakis, Ioannis","givenName":"Ioannis","familyName":"Chatzigiannakis","email":"mailto:ichatz@diag.uniroma1.it","affiliation":"Sapienza University of Rome, Italy"},{"@type":"Person","name":"Flocchini, Paola","givenName":"Paola","familyName":"Flocchini","email":"mailto:paola.flocchini@uottawa.ca","affiliation":"University of Ottawa, Canada"},{"@type":"Person","name":"Leonardi, Stefano","givenName":"Stefano","familyName":"Leonardi","email":"mailto:leonardi@diag.uniroma1.it","affiliation":"Sapienza University of Rome, Italy"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article12311","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":"#volume6335"}}}