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Synchronized planarity with applications to constrained planarity problems

Bläsius, Thomas ORCID iD icon; Fink, Simon D.; Rutter, Ignaz


We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. Synchronized Planarity then asks whether the graph admits a crossing-free embedding into the plane such that the orders of edges around synchronized vertices are consistent. We show, on the one hand, that Synchronized Planarity can be solved in quadratic time, and, on the other hand, that it serves as a powerful modeling language that lets us easily formulate several constrained planarity problems as instances of Synchronized Planarity. In particular, this lets us solve Clustered Planarity in quadratic time, where the most efficient previously known algorithm has an upper bound of O(n⁸).

Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 30.07.2021
Sprache Englisch
Identifikator KITopen-ID: 1000138420
Nachgewiesen in arXiv
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