منابع مشابه
Volume Requirements of 3D Upward Drawings
This paper studies the problem of drawing directed acyclic graphs in three dimensions in the straight-line grid model, and so that all directed edges are oriented in a common (upward) direction. We show that there exists a family of outerplanar directed acyclic graphs whose volume requirement is super-linear. We also prove that for the special case of rooted trees a linear volume upper bound is...
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Rooted trees are usually drawn planar and upward , i.e., without crossings and with parents placed above their children. In this paper we investigate the area requirement of planar upward drawings of trees, and present optimal algorithms for constructing such drawings.
متن کاملUpward Tree Drawings with Optimal
Rooted trees are usually drawn planar and upward, i.e., without crossings and without any parent placed below its child. In this paper we investigate the area requirement of planar upward drawings of rooted trees. We give tight upper and lower bounds on the area of various types of drawings, and provide linear-time algorithms for constructing optimal area drawings. Let T be a bounded-degree roo...
متن کاملLinear area upward drawings of AVL trees
We prove that any AVL tree admits a linear-area straight-line strictly-upward planar grid drawing, that is, a drawing in which (a) each edge is mapped into a single straight-line segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates. © 1998 Elsevier Science B.V.
متن کاملUpward Three-Dimensional Grid Drawings of Graphs
A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. Our first main result is that every nvertex graph with bounded degeneracy has a three-dimensional grid drawing with O...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.12.061