Now showing items 1-6 of 6

• #### An algorithm and a core set result for the weighted euclidean one-center problem ﻿

(Institute for Operations Research and the Management Sciences (I N F O R M S), 2009)
Given a set A of m points in n-dimensional space with corresponding positive weights, the weighted Euclidean one-center problem, which is a generalization of the minimum enclosing ball problem, involves the computation of ...
• #### Computing minimum-volume enclosing axis-aligned ellipsoids ﻿

(Springer, 2008)
Given a set of points S = {x1 ,..., xm}⊂ ℝn and ε&gt;0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing S. We establish that our ...
• #### A linearly convergent linear-time first-order algorithm for support vector classification with a core set result ﻿

(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011)
We present a simple first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and. ε (0,1), the proposed algorithm computes a separating hyperplane whose ...
• #### On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids ﻿

(Elsevier, 2007)
Given A {colon equals} { a1, ..., am } ⊂ Rd whose affine hull is Rd, we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum-volume enclosing ellipsoid of A. ...
• #### On the minimum volume covering ellipsoid of ellipsoids ﻿

(Society for Industrial and Applied Mathematics, 2006)
Let S denote the convex hull of m full-dimensional ellipsoids in ℝn. Given ε &gt; 0 and δ &gt; 0, we study the problems of computing a (1 + ε)-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding ...
• #### Two algorithms for the minimum enclosing ball problem ﻿

(Society for Industrial and Applied Mathematics, 2008)
Given A := {a1.....am} ⊂ ℝn and ε &gt; 0, we propose and analyze two algorithms for the problem of computing a (1 + ε)-approximation to the radius of the minimum enclosing ball of A. The first algorithm is closely related ...