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dc.contributor.authorAbboud, Amir
dc.contributor.authorWilliams, Virginia Vassilevska
dc.contributor.authorYu, Huacheng
dc.date.accessioned2021-11-05T20:49:39Z
dc.date.available2021-11-05T20:49:39Z
dc.date.issued2018-01
dc.identifier.issn0097-5397
dc.identifier.issn1095-7111
dc.identifier.urihttps://hdl.handle.net/1721.1/137622
dc.description.abstract© 2018 Society for Industrial and Applied Mathematics. Due to the lack of unconditional polynomial lower bounds, it is now in fashion to prove conditional lower bounds in order to advance our understanding of the class P. The vast majority of these lower bounds are based on one of three famous hypotheses: the 3-SUM conjecture, the all pairs shortest paths (APSP) conjecture, and the Strong Exponential Time Hypothesis. Only circumstantial evidence is known in support of these hypotheses, and no formal relationship between them is known. In hopes of obtaining “less conditional” and therefore more reliable lower bounds, we consider the conjecture that at least one of the above three hypotheses is true. We design novel reductions from 3-SUM, APSP, and CNF-SAT, and derive interesting consequences of this very plausible conjecture, including tight n3−o(1) lower bounds for purely combinatorial problems about the triangles in unweighted graphs; new n1−o(1) lower bounds for the amortized update and query times of dynamic algorithms for Single-Source Reachability, Strongly Connected Components, and Max-Flow; new n1.5−o(1) lower bound for computing a set of n st-maximum-flow values in a directed graph with n nodes and Õ(n) edges; and a hierarchy of natural graph problems on n nodes with complexity nc for c ∈ (2, 3). Only slightly nontrivial consequences of this conjecture were known prior to our work. Along the way we also obtain new conditional lower bounds for the Single-Source Max-Flow problem.en_US
dc.language.isoen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en_US
dc.relation.isversionof10.1137/15m1050987en_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.sourceSIAMen_US
dc.subjectGeneral Mathematicsen_US
dc.subjectGeneral Computer Scienceen_US
dc.titleMatching Triangles and Basing Hardness on an Extremely Popular Conjectureen_US
dc.typeArticleen_US
dc.identifier.citationAbboud, Amir, Williams, Virginia Vassilevska and Yu, Huacheng. 2018. "Matching Triangles and Basing Hardness on an Extremely Popular Conjecture." 47 (3).
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2019-07-09T13:43:56Z
dspace.date.submission2019-07-09T13:43:57Z
mit.journal.volume47en_US
mit.journal.issue3en_US
mit.metadata.statusAuthority Work and Publication Information Neededen_US


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