Results 1 
3 of
3
Popular conjectures imply strong lower bounds for dynamic problems
 CoRR
"... Abstract—We consider several wellstudied problems in dynamic 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 dete ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
Abstract—We consider several wellstudied problems in dynamic 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 connectivity, 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.
Consequences of Faster Alignment of Sequences
"... Abstract. The Local Alignment problem is a classical problem with applications in biology. Given two input strings and a scoring function on pairs of letters, one is asked to find the substrings of the two input strings that are most similar under the scoring function. The best algorithms for Local ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
(Show Context)
Abstract. The Local Alignment problem is a classical problem with applications in biology. Given two input strings and a scoring function on pairs of letters, one is asked to find the substrings of the two input strings that are most similar under the scoring function. The best algorithms for Local Alignment run in time that is roughly quadratic in the string length. It is a big open problem whether substantially subquadratic algorithms exist. In this paper we show that for all ε> 0, an O(n2−ε) time algorithm for Local Alignment on strings of length n would imply breakthroughs on three longstanding open problems: it would imply that for some δ> 0, 3SUM on n numbers is in O(n2−δ) time, CNFSAT on n variables is in O((2 − δ)n) time, and Max Weight 4Clique is in O(n4−δ) time. Our result for CNFSAT also applies to the easier problem of finding the longest common substring of binary strings with don’t cares. We also give strong conditional lower bounds for the more general Multiple Local Alignment problem on k strings, under both kwise and SP scoring, and for other string similarity problems such as Global Alignment with gap penalties and normalized Longest Common Subsequence. 1
Matching triangles and basing hardness on an extremely popular conjecture
 STOC'15
, 2015
"... ..."