9 years 6 months ago
Fully dynamic metric access methods based on hyperplane partitioning
Metric access methods based on hyperplane partitioning have the advantage, compared to the ballpartitioning-based ones, that regions do not overlap. The price is less flexibility...
Gonzalo Navarro, Roberto Uribe Paredes
111views more  JCT 2007»
9 years 11 months ago
Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements
Hyperplanes of the form xj = xi + c are called affinographic. For an affinographic hyperplane arrangement in Rn, such as the Shi arrangement, we study the function f(m) that counts...
David Forge, Thomas Zaslavsky
104views more  EOR 2007»
9 years 11 months ago
Analysis of the constraint proposal method for two-party negotiations
In the constraint proposal method a mediator locates points at which the two decision makers have joint tangent hyperplanes. We give conditions under which these points are Pareto...
Mitri Kitti, Harri Ehtamo
86views more  DCG 2008»
9 years 12 months ago
Efficient Algorithms for Maximum Regression Depth
We investigate algorithmic questions that arise in the statistical problem of computing lines or hyperplanes of maximum regression depth among a set of n points. We work primarily...
Marc J. van Kreveld, Joseph S. B. Mitchell, Peter ...
9 years 12 months ago
Partial covers of PG(n, q)
In this paper, we investigate some properties of partial covers of PG(n, q). We show that a set of q + a hyperplanes, q 81, a < (q - 1)/3, or q > 13 and a (q - 10)/4, that...
Stefan M. Dodunekov, Leo Storme, Geertrui Van de V...
119views more  ANOR 2010»
9 years 12 months ago
Alternating local search based VNS for linear classification
We consider the linear classification method consisting of separating two sets of points in d-space by a hyperplane. We wish to determine the hyperplane which minimises the sum of...
Frank Plastria, Steven De Bruyne, Emilio Carrizosa
10 years 4 months ago
Multivariate regression depth
The regression depth of a hyperplane with respect to a set of n points in Rd is the minimum number of points the hyperplane must pass through in a rotation to vertical. We general...
Marshall W. Bern, David Eppstein