On the average case analysis of some satisfiability model problems
Information Sciences: an International Journal
On the probabilistic performance of algorithms for the satisfiability problem
Information Processing Letters
Polynomial-average-time satisfiability problems
Information Sciences: an International Journal
Information Sciences: an International Journal
Exploiting the deep structure of constraint problems
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A theoretical evaluation of selected backtracking algorithms
Artificial Intelligence
Backtracking and random constraint satisfaction
Annals of Mathematics and Artificial Intelligence
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
On the average similarity degree between solutions of random k-SAT and random CSPs
Discrete Applied Mathematics - Discrete mathematics and theoretical computer science (DMTCS)
Partition search for non-binary constraint satisfaction
Information Sciences: an International Journal
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In this paper we propose a random CSP model, called Model GB, which is a natural generalization of standard Model B. This paper considers Model GB in the case where each constraint is easy to satisfy. In this case Model GB exhibits non-trivial behaviour (not trivially satisfiable or unsatisfiable) as the number of variables approaches infinity. A detailed analysis to obtain an asymptotic estimate (good to 1+o(1)) of the average number of nodes in a search tree used by the backtracking algorithm on Model GB is also presented. It is shown that the average number of nodes required for finding all solutions or proving that no solution exists grows exponentially with the number of variables. So this model might be an interesting distribution for studying the nature of hard instances and evaluating the performance of CSP algorithms. In addition, we further investigate the behaviour of the average number of nodes as ir (the ratio of constraints to variables) varies. The results indicate that as ir increases, random CSP instances get easier and easier to solve, and the base for the average number of nodes that is exponential in in tends to 1 as ir approaches infinity. Therefore, although the average number of nodes used by the backtracking algorithm on random CSP is exponential, many CSP instances will be very easy to solve when ir is sufficiently large.