Fully Dynamic Four-Vertex Subgraph Counting
Fully Dynamic Four-Vertex Subgraph Counting
复制标题
全动态四顶点子图计数
DOI：
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复制
发表时间：
2021
期刊：
影响因子：
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通讯作者：
Q. Hua
中科院分区：
文献类型：
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作者：
Kathrin Hanauer;Monika Henzinger;Q. Hua
本文介绍了一项全面的研究，用于在动态图中维持所有连接的四个vertex子图的数量，我们的算法维持了确定性摊销O（M 12）的长度路径的数量连接的四个vertex子图不是确定性摊销时间o的一个集团（m 23）。包含仅与查询一起提供的任意边缘的子图以及仅考虑了固定的顶点的子图。离（条件）下限不远：基于OMV的猜想，我们表明的任何动态算法都检测到存在爪子，钻石或4循环的存在或计数长度-3路径采用更新时间ω（M 1 /2 - δ），对于4个单位和所有连接的诱导子图，我们显示了任何小的ω（m 1-δ）的下限假设静态组合4-clique stumenture的更新时间表明，对于这些子图，e（m）算法不能通过多项式因素来改进。
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic amortized O ( m 12 ) update time, and any other connected four-vertex subgraph which is not a clique in deterministic amortized update time O ( m 23 ). Queries can be answered in constant time. We also study the query times for subgraphs containing an arbitrary edge that is supplied only with the query as well as the case where only subgraphs containing a vertex s that is fixed beforehand are considered. For length-3 paths, paws, 4-cycles, and diamonds our bounds match or are not far from (conditional) lower bounds: Based on the OMv conjecture we show that any dynamic algorithm that detects the existence of paws, diamonds, or 4-cycles or that counts length-3 paths takes update time Ω( m 1 / 2 − δ ). Additionally, for 4-cliques and all connected induced subgraphs, we show a lower bound of Ω( m 1 − δ ) for any small constant δ > 0 for the amortized update time, assuming the static combinatorial 4-clique conjecture holds. This shows that the O ( m ) algorithm by Eppstein et al. [9] for these subgraphs cannot be improved by a polynomial factor.
平均情况动态子图计数的复杂性
DOI：
10.1137/1.9781611977073.23
发表时间：
2022
期刊：
Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA
影响因子：
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作者：
Henzinger, Monika;Lincoln, Andrea;and Saha, Barna
通讯作者：
and Saha, Barna
稀疏图中最短循环和路径的严格硬度
DOI：
10.1137/1.9781611975031.91
发表时间：
2018
期刊：
Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
影响因子：
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作者：
Lincoln, A.;Vassilevska Williams, V.;Williams, R.
通讯作者：
Williams, R.