A space-efficient backtrack-free representation for constraint satisfaction problems

In this paper we present a radical approach to obtaining a backtrack-free representation for a constraint satisfaction problem: remove values that lead to dead-ends. This technique does not require additional space but has the drawback of removing solutions. We investigate a number of variations on the basic algorithm including the use of seed solutions, consistency techniques, and a variety of pruning heuristics. Our experimental results indicate that a significant proportion of the solutions to the original problem can be retained especially when an optimization algorithm that specifically searches for such "good" backtrack-free representations is employed. Further extensions increase solution retention by searching for high-coverage backtrack-free representations, by removing tuples rather than values, and by combining multiple backtrack-free representations. Our approach elucidates, for the first time, a three-way trade-off between space complexity, potential backtracks, and solution loss and enables algorithms that can actively reason about the trade-off between space, backtracks, and solution loss.