Proceedings ArticleDOI
Towards polynomial lower bounds for dynamic problems
Mihai Patrascu
- pp 603-610
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This work describes a carefully-chosen dynamic version of set disjointness (the "multiphase problem"), and conjecture that it requires n^Omega(1) time per operation, and forms the first nonalgebraic reduction from 3SUM, which allows3SUM-hardness results for combinatorial problems.Abstract:
We consider a number of dynamic problems with no known poly-logarithmic upper bounds, and show that they require nΩ(1) time per operation, unless 3SUM has strongly subquadratic algorithms. Our result is modular: (1) We describe a carefully-chosen dynamic version of set disjointness (the "multiphase problem"), and conjecture that it requires n^Omega(1) time per operation. All our lower bounds follow by easy reduction. (2) We reduce 3SUM to the multiphase problem. Ours is the first nonalgebraic reduction from 3SUM, and allows 3SUM-hardness results for combinatorial problems. For instance, it implies hardness of reporting all triangles in a graph. (3) It is plausible that an unconditional lower bound for the multiphase problem can be established via a number-on-forehead communication game.read more
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References
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Journal ArticleDOI
On a class of O(n2) problems in computational geometry
Anka Gajentaan,Mark H. Overmars +1 more
TL;DR: A large class of problems is described for which it is proved that they are all at least as difficult as the following base problem 3sum: Given a set S of n integers, are there three elements of S that sum up to 0.
Book ChapterDOI
Graph-theoretic arguments in low-level complexity
TL;DR: One approach to understanding complexity issues for certain easily computable natural functions is surveyed, and the notion of rigidity does offer for the first time a reduction of relevant computational questions to noncomputional properties.
Journal ArticleDOI
A new approach to dynamic all pairs shortest paths
TL;DR: A fully dynamic algorithm for general directed graphs with non-negative real-valued edge weights that supports any sequence of operations in O(n2log3n) amortized time per update and unit worst-case time per distance query, where n is the number of vertices.
Proceedings ArticleDOI
Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs
TL;DR: The first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b are presented, which use simple data structures, and are deterministic.
Proceedings ArticleDOI
On the possibility of faster SAT algorithms
Mihai Patrascu,Ryan Williams +1 more
TL;DR: Reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems are described, showing that attaining any of the following bounds would improve the state of the art in algorithms for SAT.