发表机构
The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究A*算法在最终平台上九种标准平局打破策略的扩展计数差异，证明任意策略对存在任意大加性扩展差距，并揭示单位代价搜索中低$h$与高$h$的极值行为及权重$\alpha<1$消除敏感性。
AI 中文摘要
在A*搜索算法中，对于具有相同$f$值的节点的平局打破策略决定了A*在最终$f$层上扩展哪些状态。对于九种标准平局打破策略，我们证明在一致启发式下，每一对策略都存在正代价实例，使得每种策略相对于另一种策略具有任意大的加性扩展差距。一个参数化的单位代价网格示例也给出了在低$h$与FIFO和LIFO之间无界扩展计数比率。在单位代价搜索中，当非目标状态$h>0$时，目标附近的精确启发式值导致互补的极值结果：低$h$最小化从完美区域内常见配置出发的剩余扩展数量，而高$h$在最终平台每个$h=1$的状态都是目标前驱时最大化总扩展数量。最后，使用评估函数$f_{\alpha}=g+\alpha h$，当非目标状态$h>0$时，每个启发式权重$0\leq\alpha<1$消除了平局打破敏感性，所有平局打破策略扩展相同的状态集合。
英文摘要
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.
