Generalized Longest Simple Path Problems: Speeding up Search Using SPQR Trees

The longest simple path and snake-in-a-box are combinatorial search problems of considerable research interest. Recent work has recast these problems as special cases of a generalized longest simple path (GLSP) framework, and showed how to generate improved search heuristics for them. The greatest reduction in search effort was based on SPQR tree rules, but it was posed as an open problem how to use them optimally. Unrelated to search, a theoretical paper on the existence of simple cycles that include three given edges answers such queries in linear time with SPQR trees. These theoretical results are utilized in this paper to develop advanced heuristics and search partitioning for GLSP. Empirical results on grid-based graphs show that these heuristics can result in orders of magnitude reduction in the number of expansions, as well as significantly reduced overall runtime in most cases.