Speeding Up the Gomory-Hu Parallel Cut Tree Algorithm with Efficient Graph Contractions

Abstract

A cut tree is a combinatorial structure that represents the edge-connectivity between all pairs of nodes of an undirected graph. Cut trees have multiple applications in dependability, as they represent how much it takes to disconnect every pair of network nodes. They have been used for solving connectivity problems, routing, and in the analysis of complex networks, among several other applications. This work presents a parallel version of the classical Gomory-Hu cut tree algorithm. The algorithm is heavily based on tasks that compute the minimum cut on contracted graphs. The main contribution is an efficient strategy to compute the contracted graphs, that allows processes to take advantage of previously contracted graph instances, instead of always computing all contractions from the original input graph. The proposed algorithm was implemented using MPI and experimental results are presented for several families of graphs and show significant performance gains.

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Notes

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    The Cluster is hosted at the Central Laboratory for High Performance Computing (LCPAD) of UFPR, and is sponsored by FINEP through the CT-INFRA/UFPR projects.

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Acknowledgements

This work was partially supported by the Brazilian Research Council CNPq, Grants 311451/2016-0 and 428941/2016-8.

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Correspondence to Elias P. Duarte Jr..

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Maske, C., Cohen, J. & Duarte, E.P. Speeding Up the Gomory-Hu Parallel Cut Tree Algorithm with Efficient Graph Contractions. Algorithmica 82, 1601–1615 (2020). https://doi.org/10.1007/s00453-019-00658-6

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Keywords

  • Cut trees
  • Parallel algorithms
  • Gomory-Hu algorithm
  • Graph contractions