[Paper Review] Exponential-Binary State-Space Search

Nathan Sturtevant, Malte Helmert|arXiv (Cornell University)|Jun 7, 2019

AI-based Problem Solving and Planning10 references4 citations

TL;DR

This paper introduces exponential-binary state-space search (EBSS), a novel framework that combines exponential and binary search to efficiently determine the optimal f-cost bound in heuristic state-space search. By reducing worst-case node expansions from O(N²) to O(N log C*), EBSS improves IDA* and A*-style search with inconsistent heuristics, achieving near-oracle performance in practice while guaranteeing optimal solutions.

ABSTRACT

Iterative deepening search is used in applications where the best cost bound for state-space search is unknown. The iterative deepening process is used to avoid overshooting the appropriate cost bound and doing too much work as a result. However, iterative deepening search also does too much work if the cost bound grows too slowly. This paper proposes a new framework for iterative deepening search called exponential-binary state-space search. The approach interleaves exponential and binary searches to find the desired cost bound, reducing the worst-case overhead from polynomial to logarithmic. Exponential-binary search can be used with bounded depth-first search to improve the worst-case performance of IDA* and with breadth-first heuristic search to improve the worst-case performance of search with inconsistent heuristics.

Motivation & Objective

• To address the high worst-case time complexity of iterative deepening search when the optimal cost bound is unknown.
• To reduce the number of node expansions in IDA* and A* with inconsistent heuristics, which can suffer from quadratic overhead due to repeated re-expansion.
• To develop a general-purpose search framework that adaptively balances exploration speed and accuracy in state-space search.
• To achieve performance close to the oracle (optimal) solution cost while maintaining optimality guarantees.

Proposed method

• EBSS uses a hybrid search strategy that alternates between exponential and binary search phases to locate the optimal f-cost bound.
• It maintains lower and upper bounds on the number of node expansions to ensure the f-cost bound increases neither too slowly nor too quickly.
• The algorithm interleaves exponential growth of the f-cost bound with binary refinement to converge on the optimal cost window.
• It applies to both IDA*-style depth-first and A*-style breadth-first search, adapting to inconsistent heuristics by controlling re-expansion overhead.
• The method uses a configurable parameter Δ to control the initial exponential step size, which affects early search efficiency.
• It leverages black-box state-space access (init, is_goal, succ, cost, h) to remain general and applicable across diverse problem domains.

Experimental results

Research questions

• RQ1 Can a hybrid search strategy combining exponential and binary search reduce the worst-case node expansion overhead in iterative deepening search?
• RQ2 How does exponential-binary search compare to IDA* in terms of node expansions and runtime on problems with non-unit costs?
• RQ3 To what extent can EBSS reduce re-expansion overhead in A* with inconsistent heuristics?
• RQ4 Does EBSS achieve performance close to the oracle while still guaranteeing optimality in practice?
• RQ5 How sensitive is EBSS to parameter choices like Δ and expansion window size?

Key findings

• EBTS solved all 100 instances of the weighted 4x4 sliding tile puzzle within resource limits, while IDA* solved only 57.
• With optimal parameters, EBTS expanded only 858.6×10⁶ nodes, compared to IDA*’s 62,044.3×10⁶, reducing node expansions by a factor of ~72.
• EBTS achieved performance within a factor of three of the oracle on the 4x4 sliding tile puzzle, demonstrating near-optimal efficiency.
• In the pancake puzzle, EBTS(10,20,1e6,1e6) solved all 100 instances with only 10.3×10⁶ expansions, compared to IDA*’s 590.73×10⁶.
• On the inconsistent heuristic graph from Mérő (1984), EBGS(10,20,3) scaled to k=10,000 with only 91,625 node expansions, far below A*’s 75 million.
• EBGS achieved near-oracle performance (20,002 vs. 91,625 expansions) on the largest test instance, showing logarithmic growth in overhead.