Problem
Research questions and friction points this paper is trying to address.
repeated-edge arrival
triangle counting
graph streaming
right-to-be-forgotten
approximation
Counting Triangles in Graph Streams with Repeatable and Forgettable Edges
🤖 AI Summary
研究了图流中可重复和可遗忘边的三角形计数问题，设计了首个具有最优空间复杂度的单遍算法，并扩展到右被遗忘图流模型。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
repeated-edge arrival model
triangle counting
optimal space complexity
right-to-be-forgotten graph streaming (RFGS)
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