Simpler and Faster Directed Low-Diameter Decompositions

TL;DR

This paper introduces a more efficient and straightforward algorithm for low-diameter decompositions in directed graphs, achieving comparable theoretical guarantees with improved running time over previous methods.

Contribution

It presents a simplified and faster algorithm for directed low-diameter decompositions, matching existing theoretical bounds while reducing computational complexity.

Findings

Achieves $O(rac{m+n ext{log} ext{log} n}{ ext{log}^2 n})$ running time

Matches the $O( ext{log} n ext{log} ext{log} n)$ loss factor from prior work

Provides a more accessible approach to directed low-diameter decompositions

Abstract

We present a simpler and faster algorithm for low-diameter decompositions on directed graphs, matching the $O(\log n\log\log n)$ loss factor from Bringmann, Fischer, Haeupler, and Latypov (ICALP 2025) and improving the running time to $O((m+n\log\log n)\log^2n)$.