Parallelization of non-admissible search algorithms such as GBFS poses a challenge because straightforward parallelization can result in search behavior which significantly deviates from sequential search. Previous work proposed PUHF, a parallel search algorithm which is constrained to only expand states that can be expanded by some tie-breaking strategy for GBFS. We show that despite this constraint, the number of states expanded by PUHF is not bounded by a constant multiple of the number of states expanded by sequential GBFS with the worst-case tie-breaking strategy. We propose and experimentally evaluate One Bench At a Time (OBAT), a parallel greedy search which guarantees that the number of states expanded is within a constant factor of the number of states expanded by sequential GBFS with some tie-breaking policy.

In order to understand and control the search behavior of parallel search, recent work has proposed a class of constrained parallel greedy best-first search algorithms which only expands states that satisfy some constraint. However, enforcing such constraints can be costly, as threads must be waiting idly until a state that satisfies the expansion constraint is available. We propose an improvement to constrained parallel search which decouples state generation and state evaluation and significantly improves state evaluation rate, resulting in better search performance.

While parallelization of A* is fairly well-understood, parallelization of GBFS has been much less understood. Recent work has proposed PUHF, a parallel GBFS which restricts search to exploration of the Bench Transition System (BTS), which is the set of states that can be expanded by GBFS under some tie-breaking policy. However, PUHF causes threads to spend much of the time waiting so that only states which are guaranteed to be in the BTS are expanded. We propose improvements to PUHF which significantly reduce idle time and allow more rapid exploration of the BTS, resulting in better search performance.