Engineering Fully Dynamic Exact $\Delta$-Orientation Algorithms

TL;DR

This paper introduces the first fully dynamic algorithm for maintaining an optimal edge orientation in graphs, significantly improving update times and outperforming static algorithms in experiments.

Contribution

The paper presents a novel fully dynamic $ abla$-orientation algorithm that efficiently maintains low out-degree orientations during edge updates.

Findings

Achieves 32% lower running time compared to recent algorithms.

Update time is up to 10^6 times faster than static exact algorithms.

Maintains optimal edge orientation during both insertions and deletions.

Abstract

A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers specific queries pertinent to the problem at hand. In this work, we address the fully dynamic edge orientation problem, also known as the fully dynamic $\Delta$-orientation problem. The objective is to maintain an orientation of the edges in an undirected graph such that the out-degree of any vertex remains low. When edges are inserted or deleted, it may be necessary to reorient some edges to prevent vertices from having excessively high out-degrees. In this paper, we introduce the first algorithm that maintains an optimal edge orientation during both insertions and deletions. In experiments comparing with recent nearly exact algorithms, we achieve a 32% lower running time. The update time of our algorithm is up to 6 orders of magnitude faster than static exact algorithms.