Four-Connected Triangulations of Planar Point Sets
نویسندگان
چکیده
منابع مشابه
Four-connected triangulations of planar point sets
In this paper, we consider the problem of determining in polynomial time whether a given planar point set P of n points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing P , and present an O(n) algorithm of constructing a 4-connected triangulation of P . Thus, our algorithm solves a longstanding open problem in computational geometry and geometric...
متن کاملCounting Triangulations of Planar Point Sets
We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-fre...
متن کاملThe Number of Triangulations on Planar Point Sets
We give a brief account of results concerning the number of triangulations on finite point sets in the plane, both for arbitrary sets and for specific sets such as the n× n integer lattice. Given a finite point set P in the plane, a geometric graph is a straight line embedded graph with vertex set P where no segment realizing an edge contains points from P other than its endpoints. We are inter...
متن کاملConstrained Independence System and Triangulations of Planar Point Sets
We propose and study a new constrained independence system. We obtain a sequence of results, including a matching theorem for bases of the system and introducing a set of light elements which give a lower bound for the objective function of a minimization problem in the system. We then demonstrate that the set of triangulations of a planar point set can be modeled as constrained independence sy...
متن کاملPoint sets with planar embeddings of cubic, connected graphs
Let P be a set of n ≥ 3 points in the plane in general position with n even and let h being the number of points on the convex hull of P . We want to know in which cases P admits a planar embedding of a cubic, connected graph (a “cubic embedding”)? García et al. proved in [1] that cubic embeddings always exists for h ≤ 4n, but for higher values of h the question remained open. We present a char...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2015
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-015-9694-x