Expected size of random Tukey layers and convex layers
نویسندگان
چکیده
We study the Tukey layers and convex of a planar point set, which consists n points independently uniformly sampled from polygon with k vertices. show that expected number vertices on first t is O ( log / ) 3 2 . also lower bound Ω for both quantities in special cases where = , 4 The implications those results average-case analysis two computational geometry algorithms are then discussed.
منابع مشابه
A Simple Convex Layers Algorithm
Given a set of n points P in the plane, the first layer L1 of P is formed by the points that appear on P ’s convex hull. In general, a point belongs to layer Li, if it lies on the convex hull of the set P \ ⋃ j<i{Lj}. The convex layers problem is to compute the convex layers Li. Existing algorithms for this problem either do not achieve the optimal O (n log n) runtime and linear space, or are o...
متن کاملMinimum Pseudo-Triangulation Using Convex Hull Layers
Pseudo-triangulation is regarded as one of the most commonly used problems in computational geometry. In this paper we consider the problem of minimum pseudotriangulation of a given set of points S in the plane using convex hull layers and we propose two new methods that will lead to the production of minimum pseudo-triangulation. This means that the number of pseudo-triangles created in minimu...
متن کاملDistribution Of Maximal Layers Of Random Orders
In this paper we address the problem of computing the expected size of the different maximal layers of a random partial order. That is, given a point set P = {p1, ..., pn} with pi ∈ [0, 1] picked uniformly at random, we try to determine the expected size of successive maximal layers of P . We present an enumerative expression for this quantity when k = 2 and study its behavior for higher dimens...
متن کاملOn Maximal Layers Of Random Orders
ON MAXIMAL LAYERS OF RANDOM ORDERS Indranil Banerjee George Mason University, 2015 Thesis Director: Dr. Dana Richards In this thesis we investigate the maximal layers of random partial orders. Main contributions are two-fold. In the first half we investigate the expected size of different maximal layers of a random partial order. In particular when the points are in a plane, we give an enumerat...
متن کاملOutput-Sensitive Peeling of Convex and Maximal Layers
We give an output-sensitive algorithm to compute the first k convex or maximal layers in 0( n log I&) -time where Hk is the number of points participating in the first k layers. Computing only the first k layers is interesting in various problems that arise in computational geometry (k-sets and dually k-levels, k-hulls and dually k-belts), pattern recognition, statistics, operations research, etc.
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: Computational Geometry: Theory and Applications
سال: 2021
ISSN: ['0925-7721', '1879-081X']
DOI: https://doi.org/10.1016/j.comgeo.2021.101856