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

24 Scopus citations


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 publicationLATIN 2014
Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
Number of pages12
ISBN (Print)9783642544224
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)0302-9743
ISSN (Electronic)1611-3349


Other11th Latin American Theoretical Informatics Symposium, LATIN 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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