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Master's Dissertation
DOI
10.11606/D.45.2012.tde-07052012-164622
Document
Author
Full name
Guilherme Puglia Assunção
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Ferreira, Carlos Eduardo (President)
Cerioli, Marcia Rosana
Pina Junior, Jose Coelho de
Title in Portuguese
Representações retangulares de grafos planares
Keywords in Portuguese
desenho de grafos
desenho retangular
otimização combinatória
planaridade
representação retangular
teoria dos grafos
Abstract in Portuguese
Uma representação retangular de um grafo plano G é uma representação de G, onde cada vértice é desenhado como um retângulo de modo que dois retângulos devem compartilhar algum segmento de seus lados se e somente se existe uma aresta em G entre os vértices correspondentes aos retângulos. Ainda, a representação de G deve formar um retângulo e não deve existir buracos, ou seja, toda região interna deve corresponder a algum vértice de G. Um desenho retangular de um grafo plano H é um desenho de H, onde todas as arestas são desenhadas como segmentos horizontais ou verticais. Ainda, todas as faces internas são retângulos e as arestas que incidem na face externa também formam um retângulo. Nesta dissertação, apresentamos os principais trabalhos existentes na literatura para problemas associados à representação retangular. Também apresentamos resultados para problemas associados ao desenho retangular. Por fim, apresentamos o algoritmo que desenvolvemos para determinar as coordenadas dos vértices de um desenho retangular quando a orientação das arestas já foram determinadas.
Title in English
Rectangular representations of plane graphs
Keywords in English
combinatorial optimization
graph drawings
graph theory
planarity
rectangular drawing
rectangular representation
Abstract in English
A rectangular representation of a plane graph G is a representation of G, where each vertex is drawn as a rectangle, such as two rectangles have to share some boundary if and only if exist an edge in G between the corresponding vertices. Also, the representation of G must form a rectangle and does not contain any holes, in other words, every point inside the formed rectangle must correspond to some vertex of G. A rectangular drawing of a plane graph H is a drawing of H, where all edges are drawn either in vertical or in horizontal. Also, every internal face is a rectangle and the edges which are incident in the external face define a rectangle. In this dissertation, we present the main studies in the literature for problems associated with the rectangular representation. We also present results for problems associated with rectangular drawing. Finally, we present the algorithm we developed to determine the coordinates of the vertices of a rectangular drawing when the orientation of the edges have been determined.
 
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master.pdf (9.71 Mbytes)
Publishing Date
2012-05-08
 
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