Maximum Matching Size for Bounded Arboricity Graphs in the Dynamic Graph Stream Model using $\tilde{O}(n^{2/3})$ space

2026-09-16

AI Summary

本文提出了一种在动态图流模型中，使用约O(n^(2/3))空间的一次遍历算法来近似计算有界树宽图的最大匹配大小。

Abstract

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.

Problem

• Maximum Matching
• Bounded Arboricity
• Dynamic Graph Stream
• Approximation
• Space Complexity

Innovation

• one-pass algorithm
• maximum matching size
• bounded arboricity graphs
• dynamic graph stream model
• linear sketch