Clustered Planarity with Pipes

TL;DR

This paper investigates a generalized version of the Clustered Planarity problem, called with pipes, providing algorithms for specific cases where pipe orderings are fixed or selectable, extending previous planarity concepts.

Contribution

It introduces algorithms for deciding clustered planarity with pipes under fixed or flexible pipe orderings, broadening the applicability of planarity testing methods.

Findings

Algorithms for fixed pipe orderings

Algorithms for flexible pipe orderings

Extension of planarity concepts to pipe-based clustering

Abstract

We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for the two variants in which the order of the pipes around each cluster is given as part of the input or can be chosen by the algorithm.