An Optimal Algorithm for Product Structure in Planar Graphs

02/17/2022

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by   Prosenjit Bose, et al.

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The Product Structure Theorem for planar graphs (Dujmović et al.JACM, 67(4):22) states that any planar graph is contained in the strong product of a planar 3-tree, a path, and a 3-cycle. We give a simple linear-time algorithm for finding this decomposition as well as several related decompositions. This improves on the previous O(nlog n) time algorithm (Morin. Algorithmica, 85(5):1544–1558).