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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

We study a geometric representation problem, where we are given a set of axis-aligned rectangles (boxes) with fixed dimensions and a graph with vertex set. 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%.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages514-525
Number of pages12
Volume8392 LNCS
ISBN (Print)9783642544224
DOIs
StatePublished - 2014
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: Mar 31 2014Apr 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period3/31/144/4/14

Fingerprint

Approximation algorithms
Rectangle
Hardness
Stars
Approximation Algorithms
Profitability
Semantics
Profit
Star
Graph in graph theory
NP-complete problem
Contact
Geometric Representation
Graph Classes
Adjacency
Contact Problem
Planar graph
Overlap
Maximise
Heuristics

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Barth, L., Fabrikant, S. I., Kobourov, S. G., Lubiw, A., Nöllenburg, M., Okamoto, Y., ... Wolff, A. (2014). Semantic word cloud representations: Hardness and approximation algorithms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8392 LNCS, pp. 514-525). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_45

Semantic word cloud representations : Hardness and approximation algorithms. / Barth, Lukas; Fabrikant, Sara Irina; Kobourov, Stephen G; Lubiw, Anna; Nöllenburg, Martin; Okamoto, Yoshio; Pupyrev, Sergey; Squarcella, Claudio; Ueckerdt, Torsten; Wolff, Alexander.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8392 LNCS Springer Verlag, 2014. p. 514-525 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Barth, L, Fabrikant, SI, Kobourov, SG, Lubiw, A, Nöllenburg, M, Okamoto, Y, Pupyrev, S, Squarcella, C, Ueckerdt, T & Wolff, A 2014, Semantic word cloud representations: Hardness and approximation algorithms. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8392 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8392 LNCS, Springer Verlag, pp. 514-525, 11th Latin American Theoretical Informatics Symposium, LATIN 2014, Montevideo, Uruguay, 3/31/14. https://doi.org/10.1007/978-3-642-54423-1_45
Barth L, Fabrikant SI, Kobourov SG, Lubiw A, Nöllenburg M, Okamoto Y et al. Semantic word cloud representations: Hardness and approximation algorithms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8392 LNCS. Springer Verlag. 2014. p. 514-525. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-54423-1_45
Barth, Lukas ; Fabrikant, Sara Irina ; Kobourov, Stephen G ; Lubiw, Anna ; Nöllenburg, Martin ; Okamoto, Yoshio ; Pupyrev, Sergey ; Squarcella, Claudio ; Ueckerdt, Torsten ; Wolff, Alexander. / Semantic word cloud representations : Hardness and approximation algorithms. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8392 LNCS Springer Verlag, 2014. pp. 514-525 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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