Efficient fully dynamic approximate matching

Develop an efficient fully dynamic algorithm for maintaining a $(1+\epsilon)$-approximate matching with polylogarithmic, or even $n^{1-\Omega(1)}$, update time.

Background

The paper identifies fully dynamic approximate matching as a fundamental barrier to extending its decremental load-balancing results. Even though matching is simpler than load balancing, the authors state that efficient fully dynamic $(1+\epsilon)$-approximation algorithms are not known. They also note conditional lower bounds against such algorithms under polynomial dependence on $1/\epsilon$.

Because a $(1+\epsilon)$-approximate fractional load-balancing algorithm would imply comparable fully dynamic integral matching bounds, resolving this matching problem is presented as a prerequisite for obtaining a near-optimal fully dynamic load-balancing algorithm.