Recognizing rectangle of influence drawable graphs (extended abstract)

  • H. ElGindy
  • G. Liotta
  • A. Lubiw
  • H. Meijer
  • S. H. Whitesides
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)

Abstract

Given two points x and y in the plane the rectangle of influence of x and y is the axis-aligned rectangle having x and y at opposite corners. The rectangle of influence drawing of a graph G is a straight-line drawing of G such that (i) for each pair of adjacent vertices u, v of G the rectangle of influence of the points representing u and v is empty (i.e. does not contain any other point representing any other vertex of G except possibly the two representing u and v) and (ii) for each pair of non adjacent vertices u, v of G the rectangle of influence of the points representing u and v is not empty. In this paper we consider several classes of graphs, and we characterize, for each class, which graphs of the class have a rectangle of influence drawing. For each class we show that the problem of testing whether a graph G has a rectangle of influence drawing can be done in linear time. Furthermore, if the test for G is affirmative, a rectangle of influence drawing of G can be constructed in linear time with the real RAM model of computation.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. ElGindy
    • 1
  • G. Liotta
    • 2
  • A. Lubiw
    • 3
  • H. Meijer
    • 4
  • S. H. Whitesides
    • 5
  1. 1.Department of Computer ScienceThe University of NewcastleCallaghanAustralia
  2. 2.Dipartimento di Informatica e SistemisticaUniversitá di Roma ‘La Sapienza’RomaItalia
  3. 3.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  4. 4.Computing and Information Science DepartmentQueen's UniversityKingstonCanada
  5. 5.School of Computer ScienceMcGill UniversityMontréalCanada

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