静态大图的平均距离近似

中文摘要 AI 辅助

计算大规模网络中的平均距离在计算上十分密集，且受限于有限的主内存，这给图分析带来了重大挑战。本研究探索并评估了两种估计平均距离的主要方法：基于图采样的方法（随机游走，Random Walk）和基于地标（landmark）的方法，包括规模估计框架（Size Estimation Framework，SEF）与Eppstein-Wang（EW）算法。研究发现，随机游走在样本量较小时不可靠，而对于较大样本量则计算成本高昂，要达到准确性至少需要15%的节点。基于地标的方法利用HyperLogLog等概率数据结构实现内存高效的邻居探索，表现出更优的性能；其中，SEF算法具备更好的内存效率，而EW算法在计算时间更短的情况下实现了更高的准确性。在静态、无向、无权图（包括单分图和二分图）上开展的实验显示，EW算法的结果误差低至0.02%。此外，在大多数大图中，随机选取的100个节点子集足以实现准确估计。研究结果表明，EW算法为平均距离估计提供了一种实用且可扩展的解决方案，其在单分图上的可靠性优于二分图。

英文摘要

Calculating average distances in large-scale networks is computationally intensive and constrained by limited main memory, posing a significant challenge in graph analytics. This study explores and evaluates two primary approaches for estimating average distances: a graph sampling-based method (Random Walk) and landmark-based methods, including the Size Estimation Framework (SEF) and the Eppstein-Wang (EW) algorithm. Random Walk was found to be unreliable for small sample sizes and computationally expensive for larger ones, requiring at least 15% of nodes for accuracy. Landmark-based approaches, leveraging probabilistic data structures like HyperLogLog for memory-efficient neighbor exploration, demonstrated superior performance. Among these, the SEF algorithm offers better memory efficiency, while the EW algorithm achieves higher accuracy with lower computation time. Experiments on static, undirected, and unweighted graphs (both unipartite and bipartite) revealed that the EW algorithm produced results with an error margin as low as 0.02%. Additionally, a subset of 100 randomly selected nodes was sufficient for accurate estimations in most large graphs. The findings indicate that the EW algorithm provides a practical and scalable solution for average distance estimation, with higher reliability on unipartite graphs compared to bipartite graphs.

发表机构

• Leiden University（莱顿大学）
• Leiden Institute of Advanced Computer Science（莱顿高级计算机科学研究所）

机构由 AI 辅助整理，请以论文原文为准。