Greedy Rectilinear Drawings

  • Patrizio Angelini
  • Michael A. Bekos
  • Walter Didimo
  • Luca Grilli
  • Philipp KindermannEmail author
  • Tamara Mchedlidze
  • Roman Prutkin
  • Antonios Symvonis
  • Alessandra Tappini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)


A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been widely studied under different topological and geometric constraints, such as planarity, face convexity, and drawing succinctness. We introduce greedy rectilinear drawings, in which each edge is either a horizontal or a vertical segment. These drawings have several properties that improve human readability and support network routing. We address the problem of testing whether a planar rectilinear representation, i.e., a plane graph with specified vertex angles, admits vertex coordinates that define a greedy drawing. We provide a characterization, a linear-time testing algorithm, and a full generative scheme for universal greedy rectilinear representations, i.e., those for which every drawing is greedy. For general greedy rectilinear representations, we give a combinatorial characterization and, based on it, a polynomial-time testing and drawing algorithm for a meaningful subset of instances.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Michael A. Bekos
    • 1
  • Walter Didimo
    • 2
  • Luca Grilli
    • 2
  • Philipp Kindermann
    • 3
    Email author
  • Tamara Mchedlidze
    • 4
  • Roman Prutkin
    • 4
  • Antonios Symvonis
    • 5
  • Alessandra Tappini
    • 2
  1. 1.Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Università degli Studi di PerugiaPerugiaItaly
  3. 3.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  4. 4.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany
  5. 5.School of Applied Mathematical and Physical Sciences, NTUAAthensGreece

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