Let Pn be a set of n points on the plane in general position, n ≥ 4. A convex quadrangulation of Pn is a partitioning of the convex hull Conv(Pn) of Pn into a set of quadrilaterals such that their vertices are elements of Pn, and no element of Pn lies in the interior of any quadrilateral. It is straightforward to see that if P admits a quadrilaterization, its convex hull must have an even numbe...

This paper describes a new algorithm of computing the convex hull of a 3-dimensional object. The convex hull generated by this algorithm is an abstract polyhedron being described by a new data structure, the cell list, suggested by one of the authors. The correctness of the algorithm is proved and experimental results are presented.

We solve the special case of the Euclidean Traveling Salesman Problem where II m cities lie on the boundary of the convex hull of all n cities, and the other m cities lie on a line segment inside this convex hull by an algorithm which needs O(mn) time and O(n) space.

We give a simple O(n log n) algorithm to compute the convex hull of the (possibly Θ(n)) intersection points in an arrangement of n line segments in the plane. We also show an arrangement of dn planes in d-dimensions whose arrangement has Θ(nd−1) intersection points on the convex hull.

This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by discrete-time delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the original state space (also called D-invariant sets) by...

1. This note summarizes a paper [4] to appear in full elsewhere. It presents an algorithm for the minimization of a general (not necessarily differentiable) convex function. Its central idea is the construction of descent directions as projections of the origin onto the convex hull of previously calculated subgradients as long as satisfactory progress can be made. Using projection to obtain a d...

Developments in data storage technologies and image acquisition methods have led to the assemblage of large data banks. Management of these large chunks of data in an efficient manner is a challenge. Content-based Image Retrieval (CBIR) has emerged as a solution to tackle this problem. CBIR extracts images that match the query image from large image databases, based on the content. In this pape...

Let K ⊂ R d be a sufficiently round convex body (the ratio of the circumscribed ball to the inscribed ball is bounded by a constant) of a sufficiently large volume. We investigate the randomized integer convex hull I L (K) = conv(K ∩L), where L is a randomly translated and rotated copy of the integer lattice Z d. We estimate the expected number of vertices of I L (K), whose behaviour is similar...

An interior point of a nite point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k 1, let g(k) be the smallest integer such that every set of points in the plane, no three collinear, containing at least g(k) interior points has a subset of points containing exactly k interior points. We prove that g(1) = 1, g(2) = 4, g(3) 8, and g(k) k + 2; ...

In the context of N. Brown’s Hom(N,RU ), we establish that given π : N → RU , the dimension of the minimal face containing [π] is one less than the dimension of the center of the relative commutant of π. We also show the “convex independence”of extreme points in the sense that the convex hull of n extreme points is an n-vertex simplex. Along the way, we establish a version of Schur’s Lemma for ...