Random Constraint Satisfaction Problems

Details Random Constraint Satisfaction Problems Random Constraint Satisfaction Problems

2009-11-12

arxiv.org/abs/0911.2322v1

EPTCS 9, 2009, pp. 32-37

Computer Science

Discrete Mathematics

Scientific paper

10.4204/EPTCS.9.4

Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with probability close to one due to non-constructive arguments. However, no algorithms are known to find solutions efficiently with a non-vanishing probability at even much lower densities. This fact appears to be related to a phase transition in the set of all solutions. The goal of this extended abstract is to provide a perspective on this phenomenon, and on the computational challenge that it poses.

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