Algorithmica

, Volume 77, Issue 4, pp 1022–1059 | Cite as

Strip Planarity Testing for Embedded Planar Graphs

  • Patrizio Angelini
  • Giordano Da Lozzo
  • Giuseppe Di Battista
  • Fabrizio Frati
Article

Abstract

In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph G(VE) and a function \(\gamma :V \rightarrow \{1,2,\dots ,k\}\) and asks whether a planar drawing of G exists such that each edge is represented by a curve that is monotone in the y-direction and, for any \(u,v\in V\) with \(\gamma (u)<\gamma (v)\), it holds that \(y(u)<y(v)\). The problem has strong relationships with some of the most deeply studied variants of the planarity testing problem, such as clustered planarity, upward planarity, and level planarity. Most notably, we provide a polynomial-time reduction from strip planarity testing to clustered planarity. We show that the strip planarity testing problem is polynomial-time solvable if G has a prescribed combinatorial embedding.

Keywords

Planarity Clustered planarity Upward planarity  Level planarity Embedded graphs 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Wilhelm-Schickard-Institut für InformatikTübingen UniversityTübingenGermany
  2. 2.Department of EngineeringRoma Tre UniversityRomeItaly

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