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arXiv 2602.22976cs.DS
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超图匹配的高效并行算法

Efficient Parallel Algorithms for Hypergraph Matching

Heidelberg University（海德堡大学）；University of Hawaii at Manoa（夏威夷大学马诺阿分校）

Henrik Reinstädtler, Christian Schulz, Nodari Sitchinava, Fabian Walliser

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AI总结：

本文提出高效的并行算法用于超图中的最大匹配计算，通过并行识别局部最大边并加入匹配，分别在CRCW PRAM和CREW PRAM模型中实现不同时间复杂度和工作量的算法，并证明了1/d的近似保证。

摘要：

本文提出高效的并行算法用于超图中的最大匹配计算，通过并行识别局部最大边并加入匹配，在CRCW PRAM模型中实现$O(\log{\logΔ}\log{m})$时间复杂度和$O(κ\log {m})$工作量的算法，在CREW PRAM模型中实现$O((\logΔ+\log{d})\log{m})$时间复杂度和$O(κ\log {m})$工作量的算法，并证明了1/d的近似保证。

英文摘要：

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

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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