TY - GEN

T1 - Linear-time algorithms for hole-free rectilinear proportional contact graph representations

AU - Alam, Muhammad Jawaherul

AU - Biedl, Therese

AU - Felsner, Stefan

AU - Gerasch, Andreas

AU - Kaufmann, Michael

AU - Kobourov, Stephen G.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-25591-5_30

DO - 10.1007/978-3-642-25591-5_30

M3 - Conference contribution

AN - SCOPUS:84055200211

SN - 9783642255908

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

SP - 281

EP - 291

BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings

T2 - 22nd International Symposium on Algorithms and Computation, ISAAC 2011

Y2 - 5 December 2011 through 8 December 2011

ER -