Applications of generalized matrix searching to geometric algorithms

Geometric Patterns: Algorithms and Applications

We review definitions of various concept classes called geometric patterns, which are based on a measure of visual similarity called the Hausdorff metric. These classes generalize multipleinstance learning models, and have possible applications to areas including robot vision, drug activity prediction, and content-based image retrieval. We also briefly describe algorithms (which have provable g...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Geometric source separation: algorithms and applications

Optimal Algorithms for Generalized Matrix Search Problem

We present a set of optimal and asymptotically optimal sequential and parallel algorith ms for the problem of searching on an m n sorted matrix m n Our two sequential algo rithms have a time complexity ofO m log n m which is shown to be optimal Our parallel algorithm runs in O log logm log logm log n m z time usingm log logm log logm processors on a COMMON CRCW PRAM where z is a monotonically d...

Greedy Geometric Algorithms for Collections of Balls, with Applications to Geometric Approximation and Molecular Coarse-Graining

Choosing balls which best approximate a 3D object is a non trivial problem. To answer it, we first address the inner approximation problem, which consists of approximating an object FO defined by a union of n balls with k < n balls defining a region FS ⊂ FO. This solution is further used to construct an outer approximation enclosing the initial shape, and an interpolated approximation sandwiche...