图流中可重复与可遗忘边的三角形计数
Counting Triangles in Graph Streams with Repeatable and Forgettable Edges
- Indian Statistical Institute（印度统计研究所）
- Iowa State University（爱荷华州立大学）
- Reykjavik University（雷克雅未克大学）
- University of Nebraska–Lincoln（内布拉斯加大学林肯分校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对图流中边可重复到达的现实场景，提出具有最优空间复杂度的三角形计数算法，并扩展至可遗忘边模型，实现单遍及常数遍近似计算。
中文摘要 AI 辅助
大多数现有的图流算法假设理想场景，即每条边仅到达一次。现实世界的图流，如通信或事务日志，通常包含同一条边的多次重复出现。一般来说，为单次边到达情况开发的算法在边可以多次到达时可能会失效。受此启发，我们研究了重复边到达图流模型，其中一条边允许到达多次。在这项工作中，我们研究了重复边到达模型中的三角形计数问题：在任意边重复的情况下，近似计算底层简单图中的三角形数量。我们设计了首批具有最优空间复杂度的三角形计数算法。特别地，我们提出了一种单遍算法，以最优空间复杂度计算三角形数量的(ε,δ)-近似。我们引入了右遗忘图流(RFGS)模型，其中遗忘操作可能导致一条边的所有先前出现消失。我们证明了我们的单遍算法可以扩展到RFGS模型，并保持最优空间复杂度。最后，我们提出了最优的常数遍算法，用于计算重复边到达图流中三角形和团的数量(ε,δ)-近似。
英文摘要
Most existing graph streaming algorithms assume the ideal scenario where each edge arrives only once. Real-world graph streams, such as communication or transaction logs, often contain many repeated occurrences of the same edge. In general, the algorithms developed for the single-edge arrival case can fail when edges can arrive multiple times. Motivated by this, we study the {\em repeated-edge arrival graph streaming model} where an edge is allowed to arrive multiple times. In this work, we study the triangle counting problem in the repeated-edge arrival model: approximate the number of triangles in the underlying {\em simple graph} despite arbitrary edge repetitions. We design the first algorithms for triangle counting with optimal space complexity. In particular, we present a single-pass algorithm that computes an $(\varepsilon,δ)$-approximation of the number of triangles with optimal space complexity. We introduce {\em right-to-be-forgotten graph streaming} (RFGS) model, where a forget operation can cause all previous occurrences of an edge to disappear. We show that our single-pass algorithm can be extended to the RFGS model with optimal space complexity. Finally, we present optimal constant-pass algorithms that compute an $(\varepsilon,δ)$-approximation of the number of triangles and cliques for the repeated-edge arrival graph streams.
