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Sketched Representations and Orthogonal Planarity of Bounded Treewidth Graphs

  • Emilio Di Giacomo
  • Giuseppe Liotta
  • Fabrizio MontecchianiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

Abstract

Given a planar graph G and an integer b, OrthogonalPlanarity is the problem of deciding whether G admits an orthogonal drawing with at most b bends in total. We show that OrthogonalPlanarity can be solved in polynomial time if G has bounded treewidth. Our proof is based on an FPT algorithm whose parameters are the number of bends, the treewidth and the number of degree-2 vertices of G. This result is based on the concept of sketched orthogonal representation that synthetically describes a family of equivalent orthogonal representations. Our approach can be extended to related problems such as HV-Planarity and FlexDraw. In particular, both OrthogonalPlanarity and HV-Planarity can be decided in \(O(n^3 \log n)\) time for series-parallel graphs, which improves over the previously known \(O(n^4)\) bounds.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of PerugiaPerugiaItaly

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