Efficient Parallel Algorithms for Hypergraph Matching

TL;DR

This paper introduces efficient parallel algorithms for hypergraph matching that achieve fast theoretical running times and demonstrate significant practical speedups on GPUs, improving over traditional CPU methods.

Contribution

The paper presents novel parallel algorithms for hypergraph matching with proven theoretical bounds and practical GPU implementations showing substantial speedups.

Findings

Achieves $O(\log m)$ time in CRCW PRAM model with high probability.

Provides $O((\log \Delta + \log d)\log m)$ time in CREW PRAM model.

Experimental results show up to 76x speedup on GPU compared to single-core CPU.

Abstract

We present efficient parallel algorithms for computing maximal matchings in hypergraphs. Our algorithm finds locally maximal edges in the hypergraph and adds them in parallel to the matching. In the CRCW PRAM models our algorithms achieve $O(\log{m})$ time with $O(\kappa \log {m})$ work w.h.p. where $m$ is the number of hyperedges, and $\kappa$ is the sum of all vertex degrees. The CREW PRAM model algorithm has a running time of $O((\log{\Delta}+\log{d})\log{m})$ and requires $O(\kappa \log {m})$ work w.h.p. It can be implemented work-optimal with $O(\kappa)$ work in $O((\log{m}+\log{n})\log{m})$ time. We prove a $1/d$-approximation guarantee for our algorithms. We evaluate our algorithms experimentally by implementing and running the proposed algorithms on the GPU using CUDA and Kokkos. Our experimental evaluation demonstrates the practical efficiency of our approach on real-world hypergraph instances, yielding a speed up of up to 76 times compared to a single-core CPU algorithm.