Computing Treewidth on the GPU

TL;DR

This paper introduces a GPU-based parallel algorithm for computing graph treewidth, achieving significant speedups over CPU implementations through optimized parallel processing and Bloom filters.

Contribution

The paper presents the first GPU implementation of a treewidth algorithm based on dynamic programming, demonstrating substantial performance improvements.

Findings

Up to 77x speedup over CPU implementations

Effective use of Bloom filters for duplicate detection

Successful adaptation of treewidth computation to GPU constraints

Abstract

We present a parallel algorithm for computing the treewidth of a graph on a GPU. We implement this algorithm in OpenCL, and experimentally evaluate its performance. Our algorithm is based on an $O^*(2^{n})$-time algorithm that explores the elimination orderings of the graph using a Held-Karp like dynamic programming approach. We use Bloom filters to detect duplicate solutions. GPU programming presents unique challenges and constraints, such as constraints on the use of memory and the need to limit branch divergence. We experiment with various optimizations to see if it is possible to work around these issues. We achieve a very large speed up (up to $77\times$) compared to running the same algorithm on the CPU.