Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The BNS lower bound for multi-party protocols is nearly optimal
Information and Computation
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Rectangular matrix multiplication revisited
Journal of Complexity
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Satisfiability - Algorithms and Logic
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
An algorithm for the satisfiability problem of formulas in conjunctive normal form
Journal of Algorithms
A Duality between Clause Width and Clause Density for SAT
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Strong computational lower bounds via parameterized complexity
Journal of Computer and System Sciences
Algorithms and resource requirements for fundamental problems
Algorithms and resource requirements for fundamental problems
Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Derandomization of schuler’s algorithm for SAT
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
An improved upper bound for SAT
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Parameterized Complexity
Multiparty equality function computation in networks with point-to-point links
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Properties of realistic feature models make combinatorial testing of product lines feasible
Proceedings of the 14th international conference on Model driven engineering languages and systems
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computing a nonnegative matrix factorization -- provably
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Parameterized complexity and subexponential-time computability
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Finding efficient circuits for ensemble computation
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast hamiltonicity checking via bases of perfect matchings
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Exact weight subgraphs and the k-sum conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Faster exponential-time algorithms in graphs of bounded average degree
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Bounding the running time of algorithms for scheduling and packing problems
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
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We describe reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems. We show that attaining any of the following bounds would improve the state of the art in algorithms for SAT: • an O(nk-ε) algorithm for k-Dominating Set, for any k ≥ 3, • a (computationally efficient) protocol for 3-party set disjointness with o(m) bits of communication, • an n°(d) algorithm for d-SUM, • an O(n5-ε) algorithm for 2-SAT formulas with m = n1+0(1) clauses, where two clauses may have unrestricted length, and • an O((n + m)k-ε) algorithm for HornSat with k unrestricted length clauses. One may interpret our reductions as new attacks on the complexity of SAT, or sharp lower bounds conditional on exponential hardness of SAT.