GA for straight-line grid drawings of maximal planar graphs

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GA for straight-line grid drawings of maximal planar graphs

osting by E Abstract A straight-line grid drawing of a planar graph G of n vertices is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Finding algorithms for straight-line grid drawings of maximal planar graphs (MPGs) in the minimum area is still an elusive goal. In this paper we explore t...

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Straight-line Drawings of 1-planar Graphs

The classical Fáry’s theorem from the 1930s states that every planar graph can be drawn as a straight-line drawing. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-planar graphs with straight-line edges. A 1-planar graph is a sparse non-planar graph with at most one crossing per edge. We give a characterisation of those 1planar ...

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∗ Corresponding author. Abstract In this paper we introduce an application of genetic algorithms (GAs) with the problem of drawing of level planar graph or hierarchical planar graph, and explore the potential use of GAs to solve this particular problem. Given a l evel planar graph, we want to find a geometric position of every vertex (layout) in a straight-line grid drawing without any edge-int...

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The problem of finding straight-line drawings for planar graphs with small area is an important aspect in the context of drawing planar graphs and it has been extensively studied. In this thesis we will study the problem of finding planar straight-line grid drawings with minimum area. Our contributions to this problem are as follows: First, we will show, that the problem of finding minimum area...

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ژورنال

عنوان ژورنال: Egyptian Informatics Journal

سال: 2012

ISSN: 1110-8665

DOI: 10.1016/j.eij.2012.01.003