This paper studies the composition operator for credal sets introduced at the last ISIPTA conference in more detail. Our main attention is devoted to the relationship between a special type of compositional model, so-called perfect sequences of credal sets, and those of (precise) probability distributions, with the goal of finding the relationship between credal compositional models and credal ...

A random polytope, Kn, is the convex hull of n points chosen randomly, independently, and uniformly from a convex body K^R. It is shown here that, with high probability, Kn can be obtained by taking the convex hull of m = o(n) points chosen independently and uniformly from a small neighbourhood of the boundary of K. §

After McCallum and Avis [4] showed that the convex hull of a simple polygon P with n vertices can be constructed in O(n) time, several authors [1,2,3] devised simplified algorithms for this problem. Graham and Yao [2] presented a particularly simple and elegant one. After finding two points of the convex hull, their algorithm generated all other hull vertices using only one stack for intermedia...

Computing the convex hull of a planar set of points is one of the most extensively investigated topics in computational geometry. Our main contribution is to present the rst known general-case, time-and VLSI-optimal, algorithm for convex hull computation on meshes with multiple broadcasting. Speciically, we show that for every choice of a positive integer constant c, the convex hull of a set of...

Determining the convex hull of a point set is a basic operation for many applications of pattern recognition, image processing, statistics, and data mining. Although the corresponding point sets are often large, the convex hull operation has not been considered much in a database context, and state-of-the-art algorithms do not scale well to non main-memory resident data sets. In this paper, we ...

We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhedral description of the convex hull of each subset, and then take the convex hull of the union of these polyhedra. The resulting extended formulation is then compact, its projection is the convex hull of the original s...

The problem of finding the convex hull of a planar set of points P, that is, finding the smallest convex region enclosing P, arises frequently in computer graphics. For example, to fit P into a square or a circle, it is necessary and sufficient that H(P), the convex hull of P, fits; and since it is usually the case that H(P) has many fewer points than P has, it is a simpler object to manipulate...

The convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this ...

The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. This approach is computationally competitive with combinatorial methods. Tropical cyclic polytopes are also presented.

We consider convex functions on infinite dimensional spaces equipped with measures. Our main results give some estimates of the first and second derivatives of a convex function, where second derivatives are considered from two different points of view: as point functions and as measures.