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View all- Geissmann BGianinazzi L(2021)Parallel Minimum Cuts in Near-linear Work and Low DepthACM Transactions on Parallel Computing10.1145/34608908:2(1-20)Online publication date: 23-Aug-2021
Parallel Planar Subgraph Isomorphism and Vertex Connectivity
Pages 269 - 280
Abstract
We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a near-linear work dependency on the size of the target graph. Existing low depth algorithms do not guarantee that the work remains asymptotically the same for any constant-sized pattern. By using a connection to certain separating cycles, our subgraph isomorphism algorithm can decide the vertex connectivity of a planar graph (with high probability) in asymptotically near-linear work and poly-logarithmic depth. Previously, no sub-quadratic work and poly-logarithmic depth bound was known in planar graphs (in particular for distinguishing between four-connected and five-connected planar graphs).
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Index Terms
- Parallel Planar Subgraph Isomorphism and Vertex Connectivity
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601 pages
ISBN:9781450369350
DOI:10.1145/3350755
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View all- Geissmann BGianinazzi L(2021)Parallel Minimum Cuts in Near-linear Work and Low DepthACM Transactions on Parallel Computing10.1145/34608908:2(1-20)Online publication date: 23-Aug-2021
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