Simple algorithms for partial and simultaneous rectangular duals with given contact orientations

Steven Chaplick, Stefan Felsner, Philipp Kindermann, Jonathan Klawitter*, Ignaz Rutter, Alexander Wolff

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A rectangular dual of a graph G is a contact representation of G by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. The partial representation extension problem for rectangular duals asks whether a given partial rectangular dual can be extended to a rectangular dual, that is, whether there exists a rectangular dual where some vertices are represented by prescribed rectangles. The simultaneous representation problem for rectangular duals asks whether two (or more) given graphs that share a subgraph admit rectangular duals that coincide on the shared subgraph. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts.We describe linear-time algorithms for the partial representation extension problem and the simultaneous representation problem for rectangular duals when each input graph is given together with a REL. Both algorithms are based on formulations as linear programs, yet they have geometric interpretations and can be seen as extensions of the classic algorithm by Kant and He that computes a rectangular dual for a given graph. (C) 2022 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)66-74
Number of pages9
JournalTheoretical Computer Science
Volume919
DOIs
Publication statusPublished - 5 Jun 2022

Keywords

  • EXTENDING PARTIAL REPRESENTATIONS
  • Partial representation extension
  • Rectangular dual
  • Simultaneous representation

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