Linear-time algorithms for hole-free rectilinear proportional contact graph representations

Authors:
Muhammad Jawaherul Alam;Therese Biedl;Stefan Felsner;Andreas Gerasch;Michael Kaufmann;Stephen G. Kobourov
Affiliations:
Department of Computer Science, University of Arizona, Tucson, AZ;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada;Institut für Mathematik, Technische Universität Berlin, Berlin, Germany;Wilhelm-Schickhard-Institut für Informatik, Tübingen Universität, Tübingen, Germany;Wilhelm-Schickhard-Institut für Informatik, Tübingen Universität, Tübingen, Germany;Department of Computer Science, University of Arizona, Tucson, AZ
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

Citing 12
Cited 2

Floor-planning by graph dualization: 2-concave rectilinear modules

SIAM Journal on Computing
Embedding planar graphs on the grid

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On Floor-Plan of Plane Graphs

SIAM Journal on Computing
Compact floor-planning via orderly spanning trees

Journal of Algorithms
RecMap: Rectangular Map Approximations

INFOVIS '04 Proceedings of the IEEE Symposium on Information Visualization
On rectangular cartograms

Computational Geometry: Theory and Applications
Rectangular layouts and contact graphs

ACM Transactions on Algorithms (TALG)
Octagonal drawings of plane graphs with prescribed face areas

Computational Geometry: Theory and Applications
Orthogonal drawings for plane graphs with specified face areas

TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Orthogonal cartograms with few corners per face

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Optimal polygonal representation of planar graphs

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Drawing planar 3-trees with given face-areas

GD'09 Proceedings of the 17th international conference on Graph Drawing

Computing cartograms with optimal complexity

Proceedings of the twenty-eighth annual symposium on Computational geometry
Edge-Weighted contact representations of planar graphs

GD'12 Proceedings of the 20th international conference on Graph Drawing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algorithm for proportional contact representation of a maximal planar graph uses 12-sided rectilinear polygons and takes O(nlogn) time. We describe a new algorithm that guarantees 10-sided rectilinear polygons and runs in O(n) time. We also describe a linear-time algorithm for proportional contact representation of planar 3-trees with 8-sided rectilinear polygons and show that this is optimal, as there exist planar 3-trees that require 8-sided polygons. Finally, we show that a maximal outer-planar graph admits a proportional contact representation using rectilinear polygons with 6 sides when the outer-boundary is a rectangle and with 4 sides otherwise.