Simultaneous FPQ-ordering and hybrid planarity testing

We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic time for biconnected graphs. Our solution is based on a novel definition of fixedness that makes it possible to simplify and extend known techn...

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Bibliographic Details
Published inTheoretical computer science Vol. 874; pp. 59 - 79
Main Authors Liotta, Giuseppe, Rutter, Ignaz, Tappini, Alessandra
Format Journal Article
LanguageEnglish
Published Elsevier B.V 12.06.2021
Subjects
Graph drawing
Hybrid planarity testing
Simultaneous FPQ-ordering
Graph drawing
Simultaneous FPQ-ordering
Hybrid planarity testing
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Summary:We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic time for biconnected graphs. Our solution is based on a novel definition of fixedness that makes it possible to simplify and extend known techniques about Simultaneous PQ-Ordering. We exploit this result to study different versions of the hybrid planarity testing problem. Namely, we show polynomial-time solutions for a variant of NodeTrix Planarity with fixed sides, for PolyLink Planarity, and for Clique Planarity with fixed sides.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2021.05.012