“We study maximum matchings in fully dynamic graphs, which are graphs that undergo both edge insertions and deletions. Our focus is on algorithms that estimate the size of maximum matching after each update while spending a small time. … We show that for any fixed ε>0, a (2−2‾√−ε) approximation can be maintained in poly(logn) time per update even in general graphs. Our techniques also lead to the same approximation for general graphs in two passes of the semi-streaming setting, removing a similar gap in that setting.”

Find the paper and full list of authors at ArXiv.