{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8252","name":"On Weighted Bipartite Edge Coloring","abstract":"We study weighted bipartite edge coloring problem, which is a generalization of two classical problems: bin packing and edge coloring. This problem has been inspired from the study of Clos networks in multirate switching environment in communication networks. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite multi-graph G=(V,E) with weights\r\nw:E\\rightarrow [0,1]. The goal is to find a proper\r\nweighted coloring of the edges with as few colors as possible. An\r\nedge coloring of the weighted graph is called a proper\r\nweighted coloring if the sum of the weights of the edges incident\r\nto a vertex of any color is at most one. Chung and Ross conjectured 2m-1 colors are sufficient for a proper weighted coloring, where m denotes the minimum number of unit sized bins needed to pack the weights of all edges incident at any vertex. We give an algorithm that returns a coloring with at most \\lceil 2.2223m \\rceil colors improving on the previous result of \\frac{9m}{4} by Feige and Singh.\r\nOur algorithm is purely combinatorial and combines the K\u00f6nig's theorem for edge coloring bipartite graphs and first-fit decreasing heuristic for bin packing. However, our analysis uses configuration linear program for the bin packing problem to give the improved result.","keywords":["Edge coloring","Bin packing","Clos networks","Approximation algorithms","Graph algorithms"],"author":[{"@type":"Person","name":"Khan, Arindam","givenName":"Arindam","familyName":"Khan"},{"@type":"Person","name":"Singh, Mohit","givenName":"Mohit","familyName":"Singh"}],"position":16,"pageStart":136,"pageEnd":150,"dateCreated":"2015-12-14","datePublished":"2015-12-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Khan, Arindam","givenName":"Arindam","familyName":"Khan"},{"@type":"Person","name":"Singh, Mohit","givenName":"Mohit","familyName":"Singh"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2015.136","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6248","volumeNumber":45,"name":"35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)","dateCreated":"2015-12-14","datePublished":"2015-12-14","editor":[{"@type":"Person","name":"Harsha, Prahladh","givenName":"Prahladh","familyName":"Harsha"},{"@type":"Person","name":"Ramalingam, G.","givenName":"G.","familyName":"Ramalingam"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8252","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":"#volume6248"}}}