Browsing by Keywords "Core sets"
Now showing items 16 of 6

An algorithm and a core set result for the weighted euclidean onecenter 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 ndimensional space with corresponding positive weights, the weighted Euclidean onecenter problem, which is a generalization of the minimum enclosing ball problem, involves the computation of ... 
Computing minimumvolume enclosing axisaligned ellipsoids
(Springer, 2008)Given a set of points S = {x1 ,..., xm}⊂ ℝn and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)approximation to the minimumvolume axisaligned ellipsoid enclosing S. We establish that our ... 
A linearly convergent lineartime firstorder 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 firstorder 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 minimumvolume 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 minimumvolume 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 fulldimensional ellipsoids in ℝn. Given ε > 0 and δ > 0, we study the problems of computing a (1 + ε)approximation to the minimum volume covering ellipsoid of S and a (1 + δ)nrounding ... 
Two algorithms for the minimum enclosing ball problem
(Society for Industrial and Applied Mathematics, 2008)Given A := {a1.....am} ⊂ ℝn and ε > 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 ...