Popular conjectures imply strong lower bounds for dynamic problems

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Popular conjectures imply strong lower bounds for dynamic problems

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by Amir Abboud , Virginia Vassilevska Williams

Venue:	CoRR
Citations:	11 - 3 self

BibTeX

@ARTICLE{Abboud_popularconjectures,
    author = {Amir Abboud and Virginia Vassilevska Williams},
    title = {Popular conjectures imply strong lower bounds for dynamic problems},
    journal = {CoRR},
    year = {},
    pages = {2014}
}

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Abstract

Abstract—We consider several well-studied problems in dy-namic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1) Is the 3SUM problem on n numbers in O(n2−ε) time for some ε> 0? 2) Can one determine the satisfiability of a CNF formula on n variables and poly n clauses in O((2 − ε)npoly n) time for some ε> 0? 3) Is the All Pairs Shortest Paths problem for graphs on n vertices in O(n3−ε) time for some ε> 0? 4) Is there a linear time algorithm that detects whether a given graph contains a triangle? 5) Is there an O(n3−ε) time combinatorial algorithm for n×n Boolean matrix multiplication? The problems we consider include dynamic versions of bipartite perfect matching, bipartite maximum weight matching, single source reachability, single source shortest paths, strong connec-tivity, subgraph connectivity, diameter approximation and some nongraph problems such as Pagh’s problem defined in a recent paper by Pǎtraşcu[STOC 2010]. Index Terms—dynamic algorithms; all pairs shortest paths; 3SUM; lower bounds; I.

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