Efficient Parallel Algorithms for Hypergraph Matching

2026-02-26

AI Summary

This work addresses the performance bottleneck of hypergraph matching in large-scale parallel environments by proposing an efficient parallel algorithm based on the PRAM model. The algorithm constructs a matching by concurrently selecting locally maximal edges and, for the first time, achieves a work-optimal solution with logarithmic time complexity and a 1/d approximation guarantee under both CRCW and CREW PRAM models. We implement the algorithm on GPUs using CUDA and Kokkos, demonstrating up to a 76× speedup over a single-core CPU implementation on real-world hypergraph datasets, thereby strongly validating its theoretical advantages and practical efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• hypergraph matching
• parallel algorithms
• maximal matching
• PRAM model
• approximation guarantee

Innovation

• hypergraph matching
• parallel algorithms
• PRAM model
• GPU acceleration
• approximation guarantee