Browsing by Keywords "Core sets"

Now showing items 1-6 of 6

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

      Kumar, P.; Yıldırım, A. E. (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 

      Kumar, P.; Yıldırım, E. A. (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 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 

      Kumar, P.; Yıldırım, E. A. (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 

      Todd, M. J.; Yıldırım, E. A. (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 

      YIldırım, E. A. (Society for Industrial and Applied Mathematics, 2006)
      Let S denote the convex hull of m full-dimensional 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)n-rounding ...

    • Two algorithms for the minimum enclosing ball problem 

      Yıldırım, E. A. (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 ...