Efficient Dynamic Algorithms for Maintaining Approximate Maximum Matching in Graphs

We present a new algorithm that maintains a (1-ε)-approximate maximum matching in a fully dynamic graph, where the update-time depends on the density of a certain class of graphs called Ordered Ruzsa-Szemerédi (ORS) graphs. We also provide improved upper bounds on the density of both ORS and Ruzsa-Szemerédi (RS) graphs with linear size matchings.