Expansion Counts under Standard A* Tie-Breaking Strategies on the Final Plateau

2026-09-19

AI Summary

研究了A*算法在最终平层上不同平分策略下的扩展节点数量问题，通过一致启发式方法分析九种标准策略的性能差异，并提出一种参数化单位成本网格示例来展示极端情况。

Abstract

In the A* search algorithm, the tie-breaking strategies for nodes with the same $f$-value determines which states A* expands on the final $f$-layer. For nine standard tie-breaking strategies, we show that under a consistent heuristic, every pair has positive-cost instances favoring each strategy over the other by an arbitrarily large additive expansion gap. A parameterized unit-cost grid example also gives unbounded expansion-count ratios between low-$h$ with FIFO and LIFO. In unit-cost search with $h > 0$ at non-goals, exact heuristic values near the goal lead to complementary extremal results: low-$h$ minimizes the number of remaining expansions from a common configuration within the perfect region, while high-$h$ maximizes the total number of expansions when every final-plateau state with $h=1$ is a goal predecessor. Finally, with the evaluation function $f_α = g + αh$, when $h>0$ at non-goals, every heuristic weight $0 \leq α<1$ eliminates tie-breaking sensitivity, and all tie-breaking strategies expand the same set of states.

Problem

• A* search
• tie-breaking strategies
• f-value
• expansion counts
• heuristic

Innovation

• A* search algorithm
• tie-breaking strategies
• consistent heuristic
• expansion count
• heuristic weight