Drawing plane triangulations with few segments
نویسندگان
چکیده
منابع مشابه
Drawing Plane Triangulations with Few Segments
Dujmović, Eppstein, Suderman, and Wood showed that every 3-connected plane graph G with n vertices admits a straight-line drawing with at most 2.5n− 3 segments, which is also the best known upper bound when restricted to plane triangulations. On the other hand, they showed that there exist triangulations requiring 2n − 6 segments. In this paper we show that every plane triangulation admits a st...
متن کاملDrawing Plane Triangulations with Few Segments, pp. 40-45
Dujmović, Eppstein, Suderman, and Wood showed that every 3-connected plane graph G with n vertices admits a straight-line drawing with at most 2.5n− 3 segments, which is also the best known upper bound when restricted to plane triangulations. On the other hand, they showed that there exist triangulations requiring 2n − 6 segments. In this paper we show that every plane triangulation admits a st...
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We define the visual complexity of a plane graph drawing to be the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g. you need only one line segment to draw two collinear edges of the same vertex). We show that trees can be drawn with 3n/4 straight-line segments on a polynomial grid, and with n/2 straight-line segments on ...
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A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is decomposed into nearest-neighbour transpositions. We address the problem of minimizing the number of crossings together with the number of corners of the pat...
متن کاملDrawing Graphs with Few Arcs
Let G = (V,E) be a planar graph. An arrangement of circular arcs is called a composite arc-drawing of G, if its 1-skeleton is isomorphic to G. Similarly, a composite segment-drawing is described by an arrangement of straight-line segments. We ask for the smallest possible ground set of arcs/segments for a composite arc/segment-drawing. We present algorithms for constructing composite arc-drawin...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2019
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2018.02.003