# Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time

arXiv: https://arxiv.org/abs/2207.07438 · HTML: https://mlsanity.com/paper/2207.07438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Dynamic Algorithms for Matroid Submodular Maximization](https://mlsanity.com/paper/2306.00959/) (2023)

## Abstract (arXiv)

We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than 2. Specifically, we obtain a 1+frac1√2+ε≈ 1.707+ε approximation in bipartite graphs and a 1.973+ε approximation in general graphs. We thus answer in the affirmative the major open question first posed in the influential work of Onak and Rubinfeld (STOC'10) and repeatedly asked in the dynamic graph algorithms literature. Our randomized algorithms also work against an adaptive adversary and guarantee worst-case polylog update time, both w.h.p. Our algorithms are based on simulating new two-pass streaming matching algorithms in the dynamic setting. Our key new idea is to invoke the recent sublinear-time matching algorithm of Behnezhad (FOCS'21) in a white-box manner to efficiently simulate the second pass of our streaming algorithms, while bypassing the well-known vertex-update barrier.