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FOCS
1999
IEEE

A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems

9 years 8 months ago
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
We present a simple probabilistic algorithm for solving kSAT, and more generally, for solving constraint satisfaction problems (CSP). The algorithm follows a simple localsearch paradigm (cf. [9]): randomly guess an initial assignment and then, guided by those clauses (constraints) that are not satisfied, by successively choosing a random literal from such a clause and flipping the corresponding bit, try to find a satisfying assignment. If no satisfying assignment is found after O(n) steps, start over again. Our analysis shows that for any satisfiable k-CNF formula with n variables this process has to be repeated only t times, on the average, to find a satisfying assignment, where t is within a polynomial factor of (2(1 - 1/k))n . This is the fastest (and also the simplest) algorithm for 3-SAT known up to date. We consider also the more general case of a CSP with n variables, each variable taking at most d values, and constraints of order l, and analyze the complexity of the correspond...
Uwe Schöning
Added 03 Aug 2010
Updated 03 Aug 2010
Type Conference
Year 1999
Where FOCS
Authors Uwe Schöning
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