Parallel Planar Subgraph Isomorphism and Vertex Connectivity

(In Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'20), ACM, Jul. 2020) Best Paper Finalist (5/68)

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 graphs).

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BibTeX

@inproceedings{gianinazzi-par-sg-isomorphism, author={Lukas Gianinazzi and Torsten Hoefler}, title={{Parallel Planar Subgraph Isomorphism and Vertex Connectivity}}, year={2020}, month={Jul.}, booktitle={Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'20)}, publisher={ACM}, source={http://www.unixer.de/~htor/publications/}, }