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Publications of SPCL
|L. Gianinazzi, T. Hoefler:|
|Parallel Planar Subgraph Isomorphism and Vertex Connectivity|
(In Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'20), presented in , ACM, ISBN: , Jul. 2020, )
AbstractWe 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 graphs).