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- W3145802425 abstract "We describe a parallel algorithm for testing a graph for planarity, and for finding an embedding of a planar graph. For a graph on n vertices, the algorithm runs in O(log2 n) steps on n processors of a parallel RAM. The previous best algorithm for planarity testing in parallel polylog time ([Ja'Ja' and Simon, 82]) used a reduction to solving linear systems, and hence required Ω(n2..49...) processors by known methods, whereas our processor bounds are within a polylog factor of optimal. The most significant aspect of our parallel algorithms is the use of a sophisticated data structure for representing sets of embeddings, the PQ-tree of [Booth and Lueker, 76]. Previously no parallel algorithms for PQ-trees were known. We have efficient parallel algorithms for manipulating PQ-trees, which we use in our planarity algorithm." @default.
- W3145802425 created "2021-04-13" @default.
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- W3145802425 date "1986-10-01" @default.
- W3145802425 modified "2023-10-18" @default.
- W3145802425 title "An efficient parallel algorithm for planarity" @default.
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- W3145802425 doi "https://doi.org/10.1109/sfcs.1986.6" @default.
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