منابع مشابه
Dense point sets with many halving lines
We construct a dense point set of n points in the plane with ne( √ logn) halving lines. This improves the bound O(n log n) of Edelsbrunner, Valtr and Welzl from 1997. We also observe that the upper bound on the maximum number of halving lines of dense point set can be improved to O(n). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points...
متن کاملOn k-convex point sets
We extend the (recently introduced) notion of k-convexity of a two-dimensional subset of the Euclidean plane to finite point sets. A set of n points is ∗Corresponding author. Email addresses: [email protected] (Oswin Aichholzer), [email protected] (Franz Aurenhammer), [email protected] (Thomas Hackl), [email protected] (Ferran Hurtado), [email protected] (Alexander Pilz), pedro.ramos@uah...
متن کاملk-Sets of Convex Inclusion Chains of Planar Point Sets
Given a set V of n points in the plane, we introduce a new number of k-sets that is an invariant of V : the number of k-sets of a convex inclusion chain of V . A convex inclusion chain of V is an ordering (v1, v2, ..., vn) of the points of V such that no point of the ordering belongs to the convex hull of its predecessors. The k-sets of such a chain are then the distinct k-sets of all the subse...
متن کاملPoint sets with many non-crossing perfect matchings
The maximum number of non-crossing straight-line perfect matchings that a set of n points in the plane can have is known to be O(10.0438) and Ω∗(3n). The lower bound, due to Garćıa, Noy, and Tejel (2000), is attained by the double chain, which has Θ(3/n) such matchings. We reprove this bound in a simplified way that uses the novel notion of down-free matchings. We then apply this approach to se...
متن کاملOn Point Sets with Many Unit Distances in Few Directions
We study the problem of the maximum number of unit distances among n points in the plane under the additional restriction that we count only those unit distances that occur in a xed set of k directions taking the maximum over all sets of n points and all sets of k directions We prove that for xed k and su ciently large n n k the extremal sets are essentially sections of lattices bounded by edge...
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: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s004540010022