{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6839","name":"Tight Bounds For Distributed MST Verification","abstract":"This paper establishes tight bounds for the Minimum-weight Spanning Tree (MST) verification problem in the distributed setting. Specifically, we provide an MST verification algorithm that achieves simultaneously tilde ~O(|E|) messages and $tilde O(sqrt{n} + D) time, where |E| is the number of edges in the given graph G and D is G's diameter. On the negative side, we show that any MST verification algorithm must send Omega(|E|) messages and incur ~Omega(sqrt{n} + D) time in worst case.\r\n\r\nOur upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of Omega(|E|) messages and\r\nOmega(sqrt{n} + D) time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously tilde O(|E|) messages and \u00b4~O(sqrt{n} + D) time. Specifically, the best known time-optimal algorithm (using ~O(sqrt{n} + D) time) requires O(|E|+n^{3\/2}) messages, and the best known message-optimal algorithm (using ~O(|E|) messages) requires O(n) time.\r\nOn the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.","keywords":["distributed algorithms","distributed verification","labeling schemes","minimum-weight spanning tree"],"author":[{"@type":"Person","name":"Kor, Liah","givenName":"Liah","familyName":"Kor"},{"@type":"Person","name":"Korman, Amos","givenName":"Amos","familyName":"Korman"},{"@type":"Person","name":"Peleg, David","givenName":"David","familyName":"Peleg"}],"position":6,"pageStart":69,"pageEnd":80,"dateCreated":"2011-03-11","datePublished":"2011-03-11","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kor, Liah","givenName":"Liah","familyName":"Kor"},{"@type":"Person","name":"Korman, Amos","givenName":"Amos","familyName":"Korman"},{"@type":"Person","name":"Peleg, David","givenName":"David","familyName":"Peleg"}],"copyrightYear":"2011","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2011.69","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6212","volumeNumber":9,"name":"28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)","dateCreated":"2011-03-10","datePublished":"2011-03-10","editor":[{"@type":"Person","name":"Schwentick, Thomas","givenName":"Thomas","familyName":"Schwentick"},{"@type":"Person","name":"D\u00fcrr, Christoph","givenName":"Christoph","familyName":"D\u00fcrr"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6839","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":"#volume6212"}}}