Zooming Cautiously: Linear-Memory Heuristic Search With Node Expansion Guarantees

TL;DR

This paper presents two new linear-memory tree search algorithms with theoretical guarantees that they expand only a logarithmic factor more nodes than A*, outperforming previous methods like IDA* in worst-case scenarios, and demonstrating practical efficiency.

Contribution

The paper introduces two parameter-free linear-memory search algorithms with proven logarithmic node expansion guarantees, improving over prior quadratic guarantees of IDA*.

Findings

Algorithms expand only a logarithmic factor more nodes than A*

Empirical results show practical efficiency and robustness

Algorithms are fast and easy to implement

Abstract

We introduce and analyze two parameter-free linear-memory tree search algorithms. Under mild assumptions we prove our algorithms are guaranteed to perform only a logarithmic factor more node expansions than A* when the search space is a tree. Previously, the best guarantee for a linear-memory algorithm under similar assumptions was achieved by IDA*, which in the worst case expands quadratically more nodes than in its last iteration. Empirical results support the theory and demonstrate the practicality and robustness of our algorithms. Furthermore, they are fast and easy to implement.