Simultaneous FPQ-Ordering and Hybrid Planarity Testing

TL;DR

This paper introduces a quadratic-time algorithm for 1-Fixed Constrained Planarity in biconnected graphs, utilizing a novel fixedness concept to extend Simultaneous PQ-Ordering techniques and applying these to hybrid planarity testing variants.

Contribution

It presents a new fixedness definition enabling simplified, extended techniques for constrained planarity and hybrid planarity testing, including a relaxed NodeTrix Planarity variant.

Findings

Quadratic-time solution for 1-Fixed Constrained Planarity in biconnected graphs

Extension of Simultaneous PQ-Ordering techniques

Application to relaxed NodeTrix Planarity with fixed sides

Abstract

We study the interplay between embedding constrained planarity and hybrid planarity testing. We consider 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 new definition of fixedness that makes it possible to simplify and extend known techniques about Simultaneous PQ-Ordering. We apply these results to different variants of hybrid planarity testing, including a relaxation of NodeTrix Planarity with fixed sides, that allows rows and columns to be independently permuted.