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

TL;DR

This paper introduces a novel algorithm that efficiently maintains approximate maximum s-t flow in sparse graphs with sublinear update time, significantly advancing dynamic flow computation methods.

Contribution

It presents the first sublinear dynamic maximum flow algorithm with arbitrarily good approximation guarantees for sparse graphs.

Findings

Achieves $(1+)$-approximate maximum flow with $m^{1/2+o(1)} ^{-1/2}$ amortized update time.

First sublinear dynamic maximum flow algorithm in general sparse graphs.

Applicable to directed, unweighted graphs with edge insertions.

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.