Abstract

This paper examines the phase transition, in which the probability that there is a solution decreases from 1 to 0 as the constraints become increasingly tight, for a class of binary constraint satisfaction problems. In particular, it considers the mushy region, i.e. those values of the constraint tightness for which random samples of problems contain both soluble and insoluble instances. The paper reports a series of experiments with randomly-generated problems, using a standard search algorithm, intended to be representative of this class of algorithm. It attempts to describe the changing behaviour of these problems in more detail than the simple `easy-hard-easy' phase transition description; it relates the location of the maximum search cost to an algorithm-independent measure, namely the expected number of solutions; and it relates the phase transition phenomena observed when finding a single solution to the behaviour of the search algorithm when finding all solutions to the problem...

Citations

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