A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Rapid sampling though quantum computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A machine program for theorem-proving
Communications of the ACM
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Finite Domain Constraint Satisfaction Using Quantum Computation
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
ACM SIGACT News
On quantum versions of record-breaking algorithms for SAT
ACM SIGACT News
Counting models for 2SAT and 3SAT formulae
Theoretical Computer Science
A faster algorithm for finding maximum independent sets in sparse graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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In his seminal paper, Grover points out the prospect of faster solutions for an NP-complete problem like SAT. If there are n variables, then an obvious classical deterministic algorithm checks out all 2n truth assignments in about 2n steps, while his quantum search algorithm can find a satisfying truth assignment in about 2n/2 steps. For several NP-complete problems, many sophisticated classical algorithms have been designed. They are still exponential, but much faster than the brute force algorithms. The question arises whether their running time can still be decreased from T(n) to Õ (√T(n)) by using a quantum computer. Isolated positive examples are known, and some speed-up has been obtained for wider classes. Here, we present a simple method to obtain the full T(n) to Õ(√T(n)) speed-up for most of the many nontrivial exponential time algorithms for NP-hard problems. The method works whenever the widely used technique of recursive decomposition is employed. This included all currently known algorithms for which such a speedup has not yet been known.