Limiting the memory consumption of caching for detecting subproblem dominance in constraint problems

Abstract Solving constraint satisfaction problems often involves a large amount of redundant exploration stemming from the existence of subproblems whose information can be reused for other subproblems. Subproblem dominance is a general notion of reusability that arises when one subproblem imposes more constraints on the remaining part of the search than another subproblem and allows the search to reuse the solutions of the dominating subproblem for the dominated subproblem. The search can exploit subproblem dominance by storing the subproblems that have been explored in a cache and abandoning the current subproblem whenever the cache contains a subproblem that dominates it. While using caching makes it possible to solve problems where subproblem dominance arises orders of magnitude faster, storing all of these subproblems can require a substantial amount of memory, making it impractical in many cases. This paper analyses the dominance between different subproblems for various constraint problems, revealing that only a relatively small number of subproblems dominate other subproblems. Based on these findings, two types of strategies are proposed for reducing the number of subproblems stored in the cache: limiting the number of subproblems that can be stored in the cache and periodically cleaning up the cache. An experimental evaluation demonstrates that these strategies provide an effective instrument for reducing the memory consumption of caching, allowing it to be used on a larger scale. However, there is a trade-off between saving memory and reducing redundant exploration, as removing subproblems from the cache may prevent dominance from being detected for certain subproblems.