Parallel Greedy Best-First Search with a Bound on the Number of Expansions Relative to Sequential Search

2024-12-16

arXiv.org

AI Summary

Parallel greedy best-first search (GBFS) suffers from unbounded state expansions: naive parallelization often incurs far more expansions than the worst-case sequential GBFS. This paper introduces OBAT, the first parallel GBFS algorithm with rigorous theoretical guarantees—its expansion count is bounded by a constant factor (≤2.3) times that of sequential GBFS under a deterministic tie-breaking strategy, overcoming the fundamental lack of theoretical bounds in prior approaches such as PUHF. OBAT employs a “One Bench At a Time” deterministic scheduling mechanism, integrating heuristic-guided greedy expansion with a parallel state-space computation model. Experiments across diverse benchmark domains demonstrate predictable parallel speedup, stable and bounded expansion counts, and substantial improvement over baseline methods whose expansions grow unboundedly.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Control deviations in parallel GBFS from sequential search behavior
• Ensure bounded state expansions relative to sequential GBFS
• Propose OBAT for constant-factor expansion guarantee

Innovation

• Parallel Greedy Best-First Search with expansion bound
• OBAT ensures constant factor expansion limit
• Tie-breaking policy maintains sequential search behavior