Point-set embeddings of trees with given partial drawings
نویسندگان
چکیده
منابع مشابه
Point-set embeddings of plane 3-trees
A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight line segment. Given a set S of n points in the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits...
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A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight-line segment. Given a set S of n points on the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits...
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In this paper we consider planar L-shaped embeddings of trees in point sets, that is, planar drawings where the vertices are mapped to a subset of the given points and where every edge consists of two axis-aligned line segments. We investigate the minimum number m, such that any n vertex tree with maximum degree 4 admits a planar L-shaped embedding in any point set of size m. First we give an u...
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In an orthogeodesic embedding of a graph, each edge is embedded as an axis-parallel polyline that forms a shortest path in the `1 metric. In this paper we consider orthogeodesic plane embeddings of trees on grids. A grid is implicitly defined by a set P ⊂ R of points. Denote by ΓP the arrangement induced by all horizontal and vertical lines that pass through a point from P . When embedding a gr...
متن کاملOn Upward Drawings of Trees on a Given Grid
Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algo...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2009.01.001