Engineering Edge Orientation Algorithms

TL;DR

This paper introduces a scalable and efficient algorithmic framework for the edge orientation problem in large graphs, significantly improving performance over existing methods.

Contribution

We develop a novel, scalable algorithmic framework based on path manipulation, enhancing efficiency and outperforming current state-of-the-art solutions.

Findings

Our algorithm is on average 6.59 times faster than existing methods.

The framework effectively handles large-scale networks with millions or billions of edges.

Experimental results demonstrate significant performance improvements.

Abstract

Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This problem, which is solvable in polynomial time, arises in many applications. An ongoing challenge in edge orientation algorithms is their scalability, particularly in handling large-scale networks with millions or billions of edges efficiently. We propose a novel algorithmic framework based on finding and manipulating simple paths to face this challenge. Our framework is based on an existing algorithm and allows many algorithmic choices. By carefully exploring these choices and engineering the underlying algorithms, we obtain an implementation which is more efficient and scalable than the current state-of-the-art. Our experiments demonstrate significant performance improvements compared to state-of-the-art solvers. On average our algorithm is 6.59 times faster when compared to the state-of-the-art.