An efficient parallel algorithm for planarity
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Additional PC-Tree planarity conditions
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Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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A data structure called PC-tree is introduced as a generalization of PQ-trees. PC-trees were originally introduced in a planarity test of Shih and Hsu where they represent partial embeddings of planar graphs. PQ-trees were invented by Booth and Lueker to test the consecutive ones property in matrices. The original implementation of the PQ-tree algorithms by Booth and Lueker using nine templates in each bottom-up iteration is rather complicated. Also the complexity analysis is rather intricate. We give a very simple PC-tree algorithm with the following advantages: (1) it does not use any template; (2) it does all necessary operations at each iteration in one batch and does not involve the cumbersome bottom-up operation. PC-trees can be used naturally to test the circular ones property in matrices. And the induced PQ-tree algorithm can considerably simplify Booth and Lueker's modification of Lempel, Even and Cederbaum's planarity test.