An optimal randomized algorithm for d-variate zonoid depth

An optimal randomized algorithm for d-variate zonoid depth

A randomized linear expected-time algorithm for computing the zonoid depth (Dyckerhoff et al 1996, Mosler 2002) of a point with respect to a fixed dimensional point set is presented.

Algorithms for bivariate zonoid depth

Zonoid depth is a new notion of data depth proposed by Dy-ckerhoff et al [DKM96]. We give efficient algorithms for solving several zonoid depth problems for 2-dimensional (bi-variate) data. Data depth measures how deep or central a given point 0 in 1 3 2 is relative to a given data cloud or a probability distribution in 1 4 2. Some examples of data depth are halfspace, simplicial, convex hull p...

On the uniform consistency of the zonoid depth

Under some mild conditions on probability distribution P , if limn Pn = P weakly then the sequence of zonoid depth functions with respect to Pn converges uniformly to the zonoid depth function with respect to P . © 2015 Elsevier Inc. All rights reserved.

An optimal randomized online algorithm for reordering buffer management

We give an O(log log k)-competitive randomized online algorithm for reordering buffer management, where k is the buffer size. Our bound matches the lower bound of Adamaszek et al. (STOC 2011). Our algorithm has two stages which are executed online in parallel. The first stage computes deterministically a feasible fractional solution to an LP relaxation for reordering buffer management. The seco...

An approximation algorithm for d 1 - optimal motion of a