Linear-Time Algorithms for Hole-free Rectilinear Proportional Contact Graph Representations
نویسندگان
چکیده
منابع مشابه
Linear-Time Algorithms for Rectilinear Hole-free Proportional Contact Representations
A proportional contact representation of a planar graph is one where each vertex is represented by a simple polygon with area proportional to a given weight and adjacencies between polygons represent edges between the corresponding pairs of vertices. In this paper we study proportional contact representations that use only rectilinear polygons and contain no unused area or hole. There is an alg...
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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 algo...
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The apportionment problem deals with the fair distribution of a discrete set of k indivisible resources (such as legislative seats) to n entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. We present an O(n)-time algorithm for performing apportionment under a large class of highest averages methods. Our...
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We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Natural optimization goals for such re...
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We show that the vertex visited last by a LexBFS has eccentricity at least diam(G) − 2 for house-hole-free graphs, at least diam(G) − 1 for house-hole-domino-free graphs, and equal to diam(G) for house-hole-domino-free and AT-free graphs. To prove these results we use special metric properties of house-hole-free graphs with respect to LexBFS. ? 1999 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2013
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-013-9764-5