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dc.contributor.authorBernstein, Aaron
dc.date.accessioned2010-10-06T15:24:52Z
dc.date.available2010-10-06T15:24:52Z
dc.date.issued2009-10
dc.date.submitted2009-10
dc.identifier.isbn978-1-4244-5116-6
dc.identifier.issn0272-5428
dc.identifier.otherINSPEC Accession Number: 11207109
dc.identifier.urihttp://hdl.handle.net/1721.1/58901
dc.description.abstractFor any fixed 1 > [epsilon] > 0 we present a fully dynamic algorithm for maintaining (2 + [epsilon])-approximate all-pairs shortest paths in undirected graphs with positive edge weights. We use a randomized (Las Vegas) update algorithm (but a deterministic query procedure), so the time given is the expected amortized update time. Our query time O(log log log n). The update time is O[over ~](mnO(1/[sqrt](log n)) log (nR)), where R is the ratio between the heaviest and the lightest edge weight in the graph (so R = 1 in unweighted graphs). Unfortunately, the update time does have the drawback of a super-polynomial dependence on e. it grows as (3/[epsilon])[sqrt]log n/log(3/[epsilon]) = n [sqrt]log (3/[epsilon])/log n. Our algorithm has a significantly faster update time than any other algorithm with sub-polynomial query time. For exact distances, the state of the art algorithm has an update time of O[over ~](n[superscript 2]). For approximate distances, the best previous algorithm has a O(kmn[superscript 1/k]) update time and returns (2 k - 1) stretch paths. Thus, it needs an update time of O(m[sqrt](n)) to get close to our approximation, and it has to return O([sqrt](log n)) approximate distances to match our update time.en_US
dc.language.isoen_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/FOCS.2009.16en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceIEEEen_US
dc.subjectshortest pathsen_US
dc.subjectgraph algorithmsen_US
dc.subjectdynamic algorithmsen_US
dc.subjectapproximation algorithmsen_US
dc.titleFully dynamic (2 + epsilon) approximate all-pairs shortest paths with fast query and close to linear update timeen_US
dc.typeArticleen_US
dc.identifier.citationBernstein, Aaron. “Fully Dynamic (2 + Epsilon) Approximate All-Pairs Shortest Paths with Fast Query and Close to Linear Update Time.” IEEE, 2009. 693–702.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.approverBernstein, Aaron
dc.contributor.mitauthorBernstein, Aaron
dc.relation.journal50th Annual IEEE Symposium on Foundations of Computer Science, 2009. FOCS '09en_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsBernstein, Aaronen
mit.licensePUBLISHER_POLICYen_US


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