Efficient Parallel Algorithms for Hypergraph Matching

TL;DR

An efficient parallel algorithm that finds locally maximal edges in the hypergraph and adds them in parallel to the matching in parallel to the matching, yielding a speed up of up to 76 times compared to a single-core CPU algorithm.

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 $O((κ+ n) \log {m})$ work w.h.p. where $m$ is the number of hyperedges, and $κ$ is the sum of all vertex degrees. The CREW PRAM model algorithm has a running time of $O((\logΔ+\log{d})\log{m})$ and requires $O((κ+ n) \log {m})$ work w.h.p. It can be implemented work-optimal with $O(κ+n)$ 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.

Figures (3)

• Figure 1: Visualization for the proof of the tight lower bound in Lemma \ref{['lemma:approx_tight_bound']}. There are edges that each contain a pair of nodes $x_{i}$ and $y_{i}$ for all $i \in \{1, \dots, d\}$ with weight $1$. Additionally, all of the nodes $x_1$ to $x_{d}$ are also connected by an edge with weight $1 + \epsilon$ (blue).
• Figure 2: Results on hypergraphs. Average speedup over Greedy (left) and relative quality (to the best result) per hypergraph category for our algorithms and Stack Streamingreinstadtler2025semi.
• Figure 3: Experimental results on graphs. Speedup over LM (MPI) by birn2013efficient (left) and relative matching size per graph category.

Theorems & Definitions (12)

• lemma 1
• proof
• lemma 2
• proof
• theorem 1
• proof
• proof
• theorem 2
• theorem 3
• proof