Edge Connectivity Augmentation in Near-Linear Time

TL;DR

This paper presents a near-linear time algorithm for edge connectivity augmentation and related problems, significantly improving efficiency and closing longstanding research gaps in the field.

Contribution

It introduces an optimal near-linear time algorithm for edge connectivity augmentation and edge splitting-off problems, advancing the state of the art.

Findings

Algorithm runs in  O(m) time, optimal up to lower order terms.

Closes a long-standing research gap in edge connectivity augmentation.

Provides a practical approach for large-scale network optimization.

Abstract

We give an $\tilde{O}(m)$-time algorithm for the edge connectivity augmentation problem and the closely related edge splitting-off problem. This is optimal up to lower order terms and closes the long line of work on these problems.