Engineering Fully Dynamic Δ-Orientation Algorithms

Abstract

A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms for graph problems that are solvable in polynomial time by a static algorithm. However, while there is a large body of theoretical work on efficient dynamic graph algorithms, a lot of these algorithms were never implemented and empirically evaluated.In this work, we consider the fully dynamic edge orientation problem, also called fully dynamic Δ-orientation problem, which is to maintain an orientation of the edges of an undirected graph such that the out-degree is low. If edges are inserted or deleted, one may have to flip the orientation of some edges in order to avoid vertices having a large out-degree. While there has been theoretical work on dynamic versions of this problem, currently there is no experimental evaluation available. In this work, we close this gap and engineer a range of new dynamic edge orientation algorithms as well as algorithms from the current literature. The most successful newly proposed algorithms in this paper are based on repeatedly swapping edges with smallest degree neighbors and based on breadth-first search. Moreover, we evaluate these algorithms on real-world dynamic graphs. Generally, these algorithms outperform the algorithms currently proposed in the literature. The best algorithm considered in this paper in terms of quality, based on a simple breadth-first search, computes the optimum result more than 90% of the instances and is on average only 2.4% worse than the optimum solution.*The full version of the paper can be accessed at https://arxiv.org/abs/2301.06968