Euler Meets GPU: Practical Graph Algorithms with Theoretical Guarantees

TL;DR

This paper adapts the classical Euler tour technique for parallel graph algorithms to GPU, demonstrating its effectiveness for LCA and bridge-finding problems with both theoretical guarantees and practical performance.

Contribution

It introduces GPU-optimized Euler tour-based algorithms for LCA and bridge detection, bridging classical theory with practical GPU implementation.

Findings

Euler tour algorithms outperform heuristics on hard instances.

Algorithms match heuristics' performance on easy instances.

Theoretical guarantees are maintained in GPU implementations.

Abstract

The Euler tour technique is a classical tool for designing parallel graph algorithms, originally proposed for the PRAM model. We ask whether it can be adapted to run efficiently on GPU. We focus on two established applications of the technique: (1) the problem of finding lowest common ancestors (LCA) of pairs of nodes in trees, and (2) the problem of finding bridges in undirected graphs. In our experiments, we compare theoretically optimal algorithms using the Euler tour technique against simpler heuristics supposed to perform particularly well on typical instances. We show that the Euler tour-based algorithms not only fulfill their theoretical promises and outperform practical heuristics on hard instances, but also perform on par with them on easy instances.