Improved Approximation Algorithms for Box Contact Representations

  • Michael A. Bekos
  • Thomas C. van Dijk
  • Martin Fink
  • Philipp Kindermann
  • Stephen Kobourov
  • Sergey Pupyrev
  • Joachim Spoerhase
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)


We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit.

We show that the problem is APX-complete on bipartite graphs of bounded maximum degree. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we consider several planar graph classes (stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit.


Approximation Algorithm Bipartite Graph Planar Graph Input Graph Star Center 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Thomas C. van Dijk
    • 2
  • Martin Fink
    • 2
    • 5
  • Philipp Kindermann
    • 2
  • Stephen Kobourov
    • 3
  • Sergey Pupyrev
    • 3
    • 4
  • Joachim Spoerhase
    • 2
  • Alexander Wolff
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  2. 2.Lehrstuhl für Informatik IUniversität WürzburgGermany
  3. 3.Department of Computer ScienceUniversity of ArizonaUSA
  4. 4.Institute of Mathematics and Computer ScienceUral Federal UniversityRussia
  5. 5.Department of Computer SicenceUniversity of CaliforniaSanta BarbaraUSA

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