منابع مشابه
The dual diameter of triangulations
Let P be a simple polygon with n vertices. The dual graph T ∗ of a triangulation T of P is the graph whose vertices correspond to the bounded faces of T and whose edges connect those faces of T that share an edge. We consider triangulations of P that minimize or maximize the diameter of their dual graph. We show that both triangulations can be constructed in O(n3 log n) time using dynamic progr...
متن کاملMinimum Dual Diameter Triangulations∗
Let P be a simple planar polygon with n vertices. We would like to find a triangulation MDT(P) of P that minimizes the diameter of the dual tree. We show that MDT(P) can be constructed in O(n log n) time. If P is convex, we show that the dual of any MDT has diameter 2 · dlog2(n/3)e or 2 · dlog2(n/3)e−1, depending on the value of n. We also investigate the relation between MDT(P) and the number ...
متن کاملProperties of the dual planar triangulations
This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems, which will show the properties of the dual triangulations. Also the numeric properties of the dual planar triangulations will be examined for the sake of unde...
متن کاملParametrization of Generalized Primal-Dual Triangulations
Motivated by practical numerical issues in a number of modeling and simulation problems, we introduce the notion of a compatible dual complex to a primal triangulation, such that a simplicial mesh and its compatible dual complex (made out of convex cells) form what we call a primal-dual triangulation. Using algebraic and computational geometry results, we show that compatible dual complexes exi...
متن کاملConnectedness and diameter of dual - summary
holds for every oriented graph G. Nešetřil and Tardif have proved that DT exists if and only if T is a tree (and it is unique up to homomorphism equivalence). They have also found the following construction of DT . Proposition 1 DT defined by V (DT ) = {f : V (T ) → V (T ); (u, f(u)) ∈ E(T ) or (f(u), u) ∈ E(T ) for all u ∈ V (T )}, E(DT ) = {(f, g); for all (u, v) ∈ E(T ) we have f(u) 6= v or ...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2018
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2017.06.008