{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7242","name":"New bounds on the classical and quantum communication complexity of some graph properties","abstract":"We study the communication complexity of a number of graph properties where the edges of the graph G are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are:\r\n1. An Omega(n) lower bound on the quantum communication complexity of deciding whether an n-vertex graph G is connected, nearly matching the trivial classical upper bound of O(n log n) bits of communication.\r\n2. A deterministic upper bound of O(n^{3\/2} log n) bits for deciding if a bipartite graph contains a perfect matching, and a quantum lower bound of Omega(n) for this problem.\r\n3. A Theta(n^2) bound for the randomized communication complexity of deciding if a graph has an Eulerian tour, and a Theta(n^{3\/2}) bound for its quantum communication complexity.\r\n4. The first two quantum lower bounds are obtained by exhibiting a reduction from the n-bit Inner Product problem to these graph problems, which solves an open question of Babai, Frankl and Simon [Babai et al 1986]. The third quantum lower bound comes from recent results about the quantum communication complexity of composed functions. We also obtain essentially tight bounds for the quantum communication complexity of a few other problems, such as deciding if $G$ is triangle-free, or if G is bipartite, as well as computing the determinant of a distributed matrix.","keywords":["Graph properties","communication complexity","quantum communication"],"author":[{"@type":"Person","name":"Ivanyos, G\u00e1bor","givenName":"G\u00e1bor","familyName":"Ivanyos"},{"@type":"Person","name":"Klauck, Hartmut","givenName":"Hartmut","familyName":"Klauck"},{"@type":"Person","name":"Lee, Troy","givenName":"Troy","familyName":"Lee"},{"@type":"Person","name":"Santha, Miklos","givenName":"Miklos","familyName":"Santha"},{"@type":"Person","name":"de Wolf, Ronald","givenName":"Ronald","familyName":"de Wolf"}],"position":15,"pageStart":148,"pageEnd":159,"dateCreated":"2012-12-14","datePublished":"2012-12-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ivanyos, G\u00e1bor","givenName":"G\u00e1bor","familyName":"Ivanyos"},{"@type":"Person","name":"Klauck, Hartmut","givenName":"Hartmut","familyName":"Klauck"},{"@type":"Person","name":"Lee, Troy","givenName":"Troy","familyName":"Lee"},{"@type":"Person","name":"Santha, Miklos","givenName":"Miklos","familyName":"Santha"},{"@type":"Person","name":"de Wolf, Ronald","givenName":"Ronald","familyName":"de Wolf"}],"copyrightYear":"2012","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2012.148","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":"#article7242","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"}}}