Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results

The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependency-directed backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronological backtracking. We also illuminate some issues concerning the distribution of hard and easy constraint problems. It was previously believed that the hardest problems had a small number of constraints, but we show that this result is an artifact of chronological backtracking that does not apply to the more advanced algorithms. We then study the performance of a particular intelligent backtracking algorithm that has been of much interest: dynamic backtracking. We demonstrate experimentally that for some problems this algorithm can do more harm than good. We discuss the reason for this phenomenon, and we present a modification to dynamic backtracking that fixes the problem. We also present theoretical worst-case results. It is known that dependency-directed backtracking can solve a constraint satisfaction problem in time exponential in a particular problem parameter known as the "induced width." This algorithm, however, requires about as much space as time; that is, its space requirements also grow exponentially in this parameter. This suggests the question of whether it is possible for a polynomial-space algorithm to be exponential in the induced width. We show that for a large class of constraint satisfaction algorithms, it is not possible. That is, there is a trade-off in intelligent backtracking between space and time.