Parallel Planar Subgraph Isomorphism and Vertex Connectivity
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).
Keywords
Cite
@article{arxiv.2007.01199,
title = {Parallel Planar Subgraph Isomorphism and Vertex Connectivity},
author = {Lukas Gianinazzi and Torsten Hoefler},
journal= {arXiv preprint arXiv:2007.01199},
year = {2020}
}
Comments
To appear in: Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '20), July 15-17, 2020, Virtual Event, USA. ACM, New York, NY, USA