### 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 | LATIN 2014 |

Subtitle of host publication | Theoretical Informatics - 11th Latin American Symposium, Proceedings |

Publisher | Springer-Verlag |

Pages | 514-525 |

Number of pages | 12 |

ISBN (Print) | 9783642544224 |

DOIs | |

State | Published - Jan 1 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) |
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Volume | 8392 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings*(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