Incremental Approximate Maximum Flow in $m^{1/2+o(1)}$ update time

Abstract

We show an $(1+\epsilon )$-approximation algorithm for maintaining maximum $s$-$t$ flow under $m$ edge insertions in $m^{1/2+o(1)}{\epsilon }^{-1/2}$ amortized update time for directed, unweighted graphs. This constitutes the first sublinear dynamic maximum flow algorithm in general sparse graphs with arbitrarily good approximation guarantee.