### 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 514-525 |

Number of pages | 12 |

Volume | 8392 LNCS |

ISBN (Print) | 9783642544224 |

DOIs | |

State | Published - 2014 |

Event | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay Duration: Mar 31 2014 → Apr 4 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 8392 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 |
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Country | Uruguay |

City | Montevideo |

Period | 3/31/14 → 4/4/14 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Semantic word cloud representations

T2 - Hardness and approximation algorithms

AU - Barth, Lukas

AU - Fabrikant, Sara Irina

AU - Kobourov, Stephen G

AU - Lubiw, Anna

AU - Nöllenburg, Martin

AU - Okamoto, Yoshio

AU - Pupyrev, Sergey

AU - Squarcella, Claudio

AU - Ueckerdt, Torsten

AU - Wolff, Alexander

PY - 2014

Y1 - 2014

N2 - 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%.

AB - 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%.

UR - http://www.scopus.com/inward/record.url?scp=84899939512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899939512&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54423-1_45

DO - 10.1007/978-3-642-54423-1_45

M3 - Conference contribution

AN - SCOPUS:84899939512

SN - 9783642544224

VL - 8392 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 514

EP - 525

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -