Lix, ´ Ecole Polytechnique Et Projet Algo, Inria Rocquencourt Combinatoire Des Cartes Planaires Et Applications Algorithmiques
نویسنده
چکیده
This thesis describes algorithms on planar maps (graphs embedded in the plane without edge-crossings) based on their combinatorial properties. For several important families of planar maps (3-connected, triangulations, quadrangulations), efficient procedures of random generation, encoding, and straight-line drawing are described. In particular, the first optimal encoder for the combinatorial incidences of polygonal meshes with spherical topology is developed. Starting from a generator for 3-connected maps, a new random generator for planar graphs is introduced. The complexity of generation is the best currently known: quadratic (in expectation) for exact-size sampling and linear (in expectation) for approximatesize sampling. Finally, several straight-line drawing algorithms for planar maps are introduced. The procedures are both simple to describe and very efficient, yielding the best known grid size for two families of maps: triangulations of the 4-gon with no filled 3-cycle —called irreducible— and quadrangulations. The algorithms presented in the thesis take advantage of several combinatorial structures on planar maps (orientations, partitions into spanning trees) as well as new bijective constructions. pa st el -0 00 02 93 1, v er si on 1 27 J ul 2 01 0
منابع مشابه
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* INRIA Rocquencourt (Projet AxIS) Domaine de Voluceau Rocquencourt, B.P. 105, F-78153 Le Chesnay Cedex, France {abdourahamane.balde, yves.lechevallier}@inria.fr ** INRIA Sophia Antipolis (Projet AxIS) Route des Lucioles, B.P. 93, F-06902 Sophia Antipolis Cedex, France [email protected] ***Supélec Plateau du Moulon Service Informatique F-91192 Gif-sur-Yvette Cedex marie-aude.aufaure@sup...
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تاریخ انتشار 2007