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Parallel Maximum Cardinality Matching for General Graphs on GPUs.

Gregory Schwing1, Daniel Grosu1, Loren Schwiebert1

  • 1Department of Computer Science, Wayne State University, Detroit, MI.

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|August 9, 2024
PubMed
Summary
This summary is machine-generated.

This study presents a GPU implementation of the Micali-Vazirani algorithm for Maximum Cardinality Matching in General Graphs. It achieves significant speed-ups on sparse graphs but shows performance degradation on denser graph types.

Keywords:
CUDAGPUMicali-Vazirani algorithmgeneral graphsmatching

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Area of Science:

  • Computer Science
  • Graph Theory
  • Parallel Computing

Background:

  • Maximum Cardinality Matching in General Graphs (MCMGG) is a fundamental graph problem.
  • The Micali-Vazirani algorithm offers optimal asymptotic complexity for sparse graphs.
  • Parallelizing MCMGG on GPUs is challenging due to recursive augmenting path procedures and graph partitioning requirements.

Purpose of the Study:

  • To propose and implement a GPU-accelerated version of the Micali-Vazirani algorithm for MCMGG.
  • To address the challenges of parallelizing graph matching algorithms on GPUs.

Main Methods:

  • Implemented Micali-Vazirani algorithm on GPUs.
  • Utilized thread-parallel breadth-first search for bridge edge identification.
  • Employed block-parallel path augmentation and blossom contraction.
  • Used stack-based iterative methods for augmenting path and Union-find with shared memory allocation.

Main Results:

  • Achieved up to 15-fold speed-up on very sparse regular graphs compared to serial implementation.
  • Observed up to 5-fold slowdown on denser regular graphs.
  • Experienced a 50-fold slowdown on power-law distributed Kronecker graphs.

Conclusions:

  • The proposed GPU implementation demonstrates potential for accelerating MCMGG on specific graph structures.
  • Performance is highly dependent on graph sparsity and distribution.
  • The open-sourced implementation facilitates further research in GPU-based combinatorial graph algorithms.