3D proportional contact representations of graphs

Md Jawaherul Alam, Stephen G. Kobourov, Giuseppe Liotta, Sergey Pupyrev, Sankar Veeramoni

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

3 Scopus citations

Abstract

In 3D contact representations, the vertices of a graph are represented by 3D polyhedra and the edges are realized by non-zero-area common boundaries between corresponding polyhedra. While contact representations with cuboids have been studied in the literature, we consider a novel generalization of the problem in which vertices are represented by axis-aligned polyhedra that are union of two cuboids. In particular, we study the weighted (proportional) version of the problem, where the volumes of the polyhedra and the areas of the common boundaries realize prespecified vertex and edge weights. For some classes of graphs (e.g., outerplanar, planar bipartite, planar, complete), we provide algorithms to construct such representations for arbitrary given weights.We also show that not all graphs can be represented in 3D with axis-aligned polyhedra of constant complexity.

Original languageEnglish (US)
Title of host publicationIISA 2014 - 5th International Conference on Information, Intelligence, Systems and Applications
PublisherIEEE Computer Society
Pages27-32
Number of pages6
ISBN (Print)9781479961719
DOIs
StatePublished - Jan 1 2014
Event5th International Conference on Information, Intelligence, Systems and Applications, IISA 2014 - Chania, Crete, Greece
Duration: Jul 7 2014Jul 9 2014

Publication series

NameIISA 2014 - 5th International Conference on Information, Intelligence, Systems and Applications

Other

Other5th International Conference on Information, Intelligence, Systems and Applications, IISA 2014
CountryGreece
CityChania, Crete
Period7/7/147/9/14

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Information Systems

Cite this

Alam, M. J., Kobourov, S. G., Liotta, G., Pupyrev, S., & Veeramoni, S. (2014). 3D proportional contact representations of graphs. In IISA 2014 - 5th International Conference on Information, Intelligence, Systems and Applications (pp. 27-32). [6878773] (IISA 2014 - 5th International Conference on Information, Intelligence, Systems and Applications). IEEE Computer Society. https://doi.org/10.1109/IISA.2014.6878773