Semantic Word Cloud Representations: Hardness and Approximation Algorithms

  • Lukas Barth
  • Sara Irina Fabrikant
  • Stephen G. Kobourov
  • Anna Lubiw
  • Martin Nöllenburg
  • Yoshio Okamoto
  • Sergey Pupyrev
  • Claudio Squarcella
  • Torsten Ueckerdt
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


We study a geometric representation problem, where we are given a set \(\mathcal B\) of axis-aligned rectangles (boxes) with fixed dimensions and a graph with vertex set \(\mathcal B\). The task is to place the rectangles without overlap such that two rectangles touch if the graph contains an edge between them. We call this problem Contact Representation of Word Networks (Crown). It formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Here, we represent words by rectangles and semantic relationships by edges.

We show that Crown is strongly NP-hard even if restricted to trees and weakly NP-hard if restricted to stars. We also consider the optimization problem Max-Crown where each adjacency induces a certain profit and the task is to maximize the sum of the profits. For this problem, we present constant-factor approximations for several graph classes, namely stars, trees, planar graphs, and graphs of bounded degree. Finally, we evaluate the algorithms experimentally and show that our best method improves upon the best existing heuristic by 45%.


Approximation Algorithm Planar Graph Latent Semantic Analysis Graph Class Cycle Cover 
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

  • Lukas Barth
    • 1
  • Sara Irina Fabrikant
    • 2
  • Stephen G. Kobourov
    • 3
  • Anna Lubiw
    • 4
  • Martin Nöllenburg
    • 1
  • Yoshio Okamoto
    • 5
  • Sergey Pupyrev
    • 3
    • 9
  • Claudio Squarcella
    • 6
  • Torsten Ueckerdt
    • 7
  • Alexander Wolff
    • 8
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany
  2. 2.Department of GeographyUniversity of ZurichSwitzerland
  3. 3.Department of Computer ScienceUniversity of ArizonaUSA
  4. 4.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada
  5. 5.Dept. Comm. Engineering and InformaticsUniversity of Electro-CommunicationsJapan
  6. 6.Dipartimento di IngegneriaRoma Tre UniversityItaly
  7. 7.Department of MathematicsKarlsruhe Institute of TechnologyGermany
  8. 8.Lehrstuhl für Informatik IUniversität WürzburgGermany
  9. 9.Institute of Mathematics and Computer ScienceUral Federal UniversityRussia

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