Augmenting Edge Connectivity via Isolating Cuts

TL;DR

This paper presents a faster algorithm for increasing edge connectivity in undirected graphs using isolating cuts, reducing the running time from quadratic to near-linear in the number of edges.

Contribution

It introduces a new algorithm that leverages poly-logarithmic max-flow calls to improve the efficiency of edge augmentation and splitting off problems.

Findings

Running time improved to  O(m + n^{3/2})

Applicable to edge splitting off problem with similar efficiency

Uses isolating cuts framework for algorithm design

Abstract

We give an algorithm for augmenting the edge connectivity of an undirected graph by using the isolating cuts framework (Li and Panigrahi, FOCS '20). Our algorithm uses poly-logarithmic calls to any max-flow algorithm, which yields a running time of $\tilde O(m + n^{3/2})$ and improves on the previous best time of $\tilde O(n^2)$ (Bencz\'ur and Karger, SODA '98) for this problem. We also obtain an identical improvement in the running time of the closely related edge splitting off problem in undirected graphs.