The combination of divide-and-conquer and random sampling has proven very effective in the design of fast geometric algorithms. A flurry of efficient probabilistic algorithms have been recently discovered, based on this happy marriage. We show that all those algorithms can be derandomized with only polynomial overhead. In the process we establish results of independent interest concerning the c...

We show that there are 6 isomorphism classes of hyperplanes of the dual polar space ∆ = DW (5, 2h) which arise from the Grassmannembedding. If h ≥ 2, then these are all the hyperplanes of ∆ arising from an embedding. If h = 1, then there are 6 extra classes of hyperplanes as has been shown by Pralle [23] with the aid of a computer. We will give a computer free proof for this fact. The hyperplan...

We study an interactive model of supervised clustering introduced by Balcan and Blum [7], where the clustering algorithm has query access to a teacher. We give an efficient algorithm clustering linear functionals over finite fields, which implies the learnability of parity functions in this model. We also present an efficient clustering algorithm for hyperplanes which are a natural generalizati...

The es-splitting operation on binary matroids is a natural generalization of Slater's <em>n</em>-line splitting graphs. In this paper, we characterize the closure operator matroid M<sup>e</sup><sub>X</sub> in terms original M. We also describe ats and hyperplanes bi- nary hyperplanes, respectively

AbetractRather than iteratively manually examining a variety of pre-specified architectures, a constructive learning algorithm dynamically creates a problem-specific neural network architecture. Here we present an revised version of our parallel constructive neural network learning algorithm which constructs such an architecture. The three steps of searching for points on separating hyperplanes...

We introduce a scheme for optimally allocating a variable number of bits per LSH hyperplane. Previous approaches assign a constant number of bits per hyperplane. This neglects the fact that a subset of hyperplanes may be more informative than others. Our method, dubbed Variable Bit Quantisation (VBQ), provides a datadriven non-uniform bit allocation across hyperplanes. Despite only using a frac...