Phase Transition in Finding Multiple Solutions in Constraint Satisfaction Problems

The study of phase transitions in constraint satisfaction problems has attracted much attention recently. Most of the research so far attempts to locate the phase transition for constraint satisfaction problems in which single solution is required. Smith notes that the phase transition is only an interesting event if just one solution is required. Our study reveals that a phase transition also occurs when more than one solution to a CSP is required. Our findings indicate that its location is a function of the number of solutions required. These results are obtained by generalising some previous work done by Williams and Hogg, and Smith.