How to Reduce the Average Complexity of Convex Hull Finding Algorithms
نویسندگان
چکیده
Abstract-Let X,. . ,X. be a sequence of independent Rd-valued random vectors with a common density f The following class of convex hull finding algorithms is considered: find the extrema in a finite number of carefully chosen directions; eliminate the Xi’s that belong to the interior of the polyhedron formed by these extrema; apply an O(A(n)) worst-case complexity algorithm to find the convex hull of the remaining points. We give weak sufficient conditions that imply that the overall average complexity is O(A(n)). We also show that for the standard normal density, the average complexity is O(n) whenever A(n) = n log n.
منابع مشابه
Sweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملFinding the Convex Hull of a Simple Polygon
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...
متن کاملConvex hull: Incremental variations on the Akl-Toussaint heuristics Simple, optimal and space-saving convex hull algorithms
Convex hulls are a fundamental geometric tool used in a number of algorithms. A famous paper by Akl & Toussaint in 1978 described a way to reduce the number of points involved in the computation, which is since known as the Akl-Toussaint heuristics. This paper first studies what this heurstics really represents in terms of reduction of points and demonstrates that the optimum selection is reach...
متن کاملA Note on Finding Convex Hulls Via Maximal Vectors
The problem of :‘inding the convex huh of n points has received widespread attention in the past decade. In particular, if Xr, .,., X, are independent identically distributed random vectors from Rd with common density f, the following questions were investigated: if C is the complexity of the convex hull algorithm for X1, . . . . X, (thus, C is a random variable), then how do ess sup C (the ‘wo...
متن کاملSequential and Parallel Approximate Convex Hull Algorithms
This paper defines the area measure of the quality of approximate convex hulls and proposes two new approximate convex hull algorithms. The first one is superior to known techniques under the area measure and comparable under the distance measure and time complexity. The second algorithm is superior to all known algorithms in both area and distance measures (including the first algorithm) while...
متن کامل