Area of convex hull of matrix eigenvalues

Rectilinear Convex Hull with Minimum Area

Let P be a set of n points in the plane. We solve the problem of computing the orientations for which the rectilinear convex hull of P has minimum area in optimal ⇥(n log n) time and O(n) space. Introduction The interest in the rectilinear convex hull of planar point sets arises from the study of ortho-convexity [10], a relaxation of traditional convexity. Unlike convex regions, an ortho-convex...

Area and Perimeter of the Convex Hull of Stochastic Points

Given a set P of n points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset S of P . The random subset S is formed by drawing each point p of P independently with a given rational probability πp. For both measures of the convex hull, we show that it is #P-hard to compute the probability that the m...

Measuring Interval Efficiency in Convex Hull of Data Using DEA

Rectilinear and O-convex hull with minimum area

Let P be a set of n points in the plane and O be a set of k lines passing through the origin. We show: (1) How to compute the O-hull of P in Θ(n log n) time and O(n) space, (2) how to compute and maintain the rotated hull OHθ(P ) for θ ∈ [0, 2π) in O(kn log n) time and O(kn) space, and (3) how to compute in Θ(n log n) time and O(n) space a value of θ for which the rectilinear convex hull, RHθ(P...

Computing minimum-area rectilinear convex hull and L-shape

Article history: Received 21 February 2008 Accepted 24 February 2009 Available online 24 March 2009 Communicated by T. Asano