Efficient Parallel Ear Decomposition of Graphs with Application to Betweenness-Centrality

Parallel graph algorithms continue to attract a lotof research attention given their applications to several fields ofsciences and engineering. Efficient design and implementation ofgraph algorithms on modern manycore accelerators has to how-ever contend with a host of challenges including not being able toreach full memory system throughput and irregularity. Of late, focusing on real-world graphs, researchers are addressing thesechallenges by using decomposition and preprocessing techniquesguided by the structural properties of such graphs. In this direction, we present a new GPU algorithm forobtaining an ear decomposition of a graph. Our implementationof the proposed algorithm on an NVidia Tesla K40c improvesthe state-of-the-art by a factor of 2.3x on average on a collectionof real-world and synthetic graphs. The improved performanceof our algorithm is due to our proposed characterization thatidentifies edges of the graph as redundant for the purposes of anear decomposition. We then study an application of the ear decomposition of agraph in computing the betweenness-centrality values of nodesin the graph. We use an ear decomposition of the input graph tosystematically remove nodes of degree two. The actual computation of betweenness-centrality is done on the remaining nodesand the results are extended to nodes removed in the previousstep. We show that this approach improves the state-of-the-artfor computing betweenness-centrality on an NVidia K40c GPUby a factor of 1.9x on average over a collection of real-world graphs.

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