NDLI: Linear-Time Algorithms for Hole-free Rectilinear Proportional Contact Graph Representations

Content Provider	Springer Nature Link
Author	Alam, M. Jawaherul Biedl, Therese Felsner, Stefan Gerasch, Andreas Kaufmann, Michael Kobourov, Stephen G.
Copyright Year	2013
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 first 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. We then 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. Finally we study maximal series-parallel graphs. Here we show that O(1)-sided rectilinear polygons are not possible unless we allow holes, but 6-sided polygons can be achieved with arbitrarily small holes.
Starting Page	3
Ending Page	22
Page Count	20
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	67
Issue Number	1
e-ISSN	14320541
Language	English
Publisher	Springer US
Publisher Date	2013-03-16
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Graph drawing Contact representation Cartogram Planar graph Polygon Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Algorithms Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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