有界树arity图在动态图流模型中使用$\tilde{O}(n^{2/3})$空间的最大匹配大小
Maximum Matching Size for Bounded Arboricity Graphs in the Dynamic Graph Stream Model using $\tilde{O}(n^{2/3})$ space
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中文总结 AI 辅助
针对有界树arity图，提出单遍流算法，以$\tilde{O}(n^{2/3})$空间实现最大匹配的$(1+\varepsilon)(\alpha+2)$近似，优于先前$O(n^{4/5})$界。
中文摘要 AI 辅助
本文提出了一种在插入-删除图流模型中的单遍算法，该算法返回树arity至多为$\alpha$的图中最大匹配大小的$(1+\varepsilon)(\alpha+2)$近似值。该算法使用$O(\varepsilon^{-4/3}\alpha^{4/3}n^{2/3} \text{polylog} n)$空间。对于常数$\alpha$和$\varepsilon$，这改进了先前最佳已知空间界，从$O(n^{4/5} \text{polylog} n)$降至$O(n^{2/3} \text{polylog} n)$。该算法是一个线性草图，不需要对删除次数或中间图的树arity进行限制。
英文摘要
The paper presents a one-pass algorithm in the insert-delete graph stream model that returns a $(1+\varepsilon)(α+2)$-approximation for the size of the maximum matching in a graph of arboricity at most $α$. The algorithm uses $O(\varepsilon^{-4/3}α^{4/3}n^{2/3} \text{polylog} n)$ space. For constant $α$ and $\varepsilon$, this improves the best known previous space bound from $O(n^{4/5} \text{polylog} n)$ to $O(n^{2/3} \text{polylog} n)$. The algorithm is a linear sketch and requires no bounds on the number of deletions or on the arboricity of intermediate graphs.
