用结构景观分析最短路径算法性能,发现相似结构未必有相似速度。
Graph Instance Landscapes: When Structural Similarity Does (Not) Reflect Shortest-Path Performance

- 将图嵌入低维结构特征空间,按结构相似性聚类
- 同一结构区域内的算法运行时间差异显著,结构相似不等于性能相似
- 适合研究算法对图结构敏感性的研究人员参考
最短路径算法的基准测试通常基于异构图集的整体性能,难以揭示不同搜索范式对图结构的响应。本文采用实例景观视角,将图嵌入低成本结构特征空间并聚类为结构相似区域。研究了三类基准数据集:加权Erdős--Rényi图、随机几何(无线)图和真实道路网络。评估四种代表性最短路径求解器:无信息精确搜索(Dijkstra)、双向精确搜索(双向Dijkstra)、启发式引导精确搜索(A$^{*}$)以及双端队列策略(DEQ)。在多种特征选择方案下分析聚类鲁棒性,并使用非参数检验比较各景观区域内运行时间分布。尽管生成参数可诱导出稳定的结构区域,但特征空间相似性并不必然对应性能相似性:即使在同一区域,运行时间仍常出现显著变化。合并数据集分析显示,不同基准族占据基本不重叠的区域。结果凸显了结构景观在结构感知基准测试中的潜力与局限。
原文摘要 · Abstract (English)
Benchmarking shortest-path algorithms is commonly based on aggregate performance over heterogeneous graph sets, which limits insight into how different search paradigms react to instance structure. We adopt an instance-landscape view of graph benchmarking by embedding graphs into a low-cost structural feature space and clustering them into regions of similar structure. Three benchmark suites are studied: weighted Erdős--Rényi graphs, random geometric (wireless) graphs, and real-world road networks. We evaluate four representative shortest-path solvers spanning uninformed exact search (Dijkstra), bidirectional exact search (bidirectional Dijkstra), heuristic-guided exact search (A$^{*}$), and deque-based strategies (DEQ). Clustering robustness is analyzed under multiple feature-selection schemes, and runtime distributions are compared across landscape regions using non-parametric tests. While generator parameters induce stable structural regions, we find that feature-space similarity does not necessarily imply performance similarity: significant runtime shifts are frequently observed even within the same landscape region. A merged-suite analysis further shows that different benchmark families occupy largely disjoint regions. These results highlight both the potential and the limits of structural landscapes for the structure-aware benchmarking of shortest-path algorithms.
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