Extending Orthogonal Planar Graph Drawings Is Fixed-Parameter Tractable

Sujoy Bhore, Robert Ganian, Liana Khazaliya, Fabrizio Montecchiani, Martin Nöllenburg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for fundamental representations such as planar and beyond-planar topological drawings. In this paper, we consider the extension problem for bend-minimal orthogonal drawings of planar graphs, which is among the most fundamental geometric graph drawing representations. While the problem was known to be NP-hard, it is natural to consider the case where only a small part of the graph is still to be drawn. Here, we establish the fixed-parameter tractability of the problem when parameterized by the size of the missing subgraph. Our algorithm is based on multiple novel ingredients which intertwine geometric and combinatorial arguments. These include the identification of a new graph representation of bend-equivalent regions for vertex placement in the plane, establishing a bound on the treewidth of this auxiliary graph, and a global point-grid that allows us to discretize the possible placement of bends and vertices into locally bounded subgrids for each of the above regions.

Original languageEnglish
Title of host publication39th International Symposium on Computational Geometry, SoCG 2023
EditorsErin W. Chambers, Joachim Gudmundsson
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772730
DOIs
StatePublished - 1 Jun 2023
Externally publishedYes
Event39th International Symposium on Computational Geometry, SoCG 2023 - Dallas, United States
Duration: 12 Jun 202315 Jun 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume258
ISSN (Print)1868-8969

Conference

Conference39th International Symposium on Computational Geometry, SoCG 2023
Country/TerritoryUnited States
CityDallas
Period12/06/2315/06/23

Keywords

  • bend minimization
  • extension problems
  • orthogonal drawings
  • parameterized complexity

ASJC Scopus subject areas

  • Software

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