arXiv:2608.16916cs.DScs.AI2026-08

提出高效估算大规模图平均距离的方法,误差低至0.02%。

Average Distance Approximation for Static Large Graphs

  • 采用地标法结合概率数据结构,提升内存效率
  • 仅需100个随机节点即可实现高精度估计
  • Eppstein-Wang算法在准确性和速度上表现最优

在大规模网络中计算平均距离存在计算开销大、内存受限的问题。本文评估了基于图采样的随机游走方法和基于地标的SEF与Eppstein-Wang(EW)算法。随机游走对小样本不可靠,大样本代价高,需至少15%节点才达标。而地标方法借助HyperLogLog等概率结构,在内存效率上表现更优。其中,SEF更省内存,EW在计算时间少、精度高方面领先,误差最低达0.02%。实验显示,仅用100个随机节点即可在多数大型图中实现准确估计。结果显示,EW算法在无向无权图中具可扩展性,且在单部图上的可靠性高于双部图。

原文摘要 · Abstract (English)

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.

图分析平均距离采样算法内存效率

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