Pattern sorting: A computer-controlled multidimensional sorting method using k-d trees

Stack Sorting, Trees, and Pattern Avoidance

The subject of pattern avoiding permutations has its roots in computer science, namely in the problem of sorting a permutation through a stack. A formula for the number of permutations of length n that can be sorted by passing it twice through a stack (where the letters on the stack have to be in increasing order) was conjectured by West, and later proved by Zeilberger. Goulden and West found a...

A Brief Look into Spike Sorting Methods

Spike sorting is a class of techniques used in the analysis of electrophysiological data. Studying the dynamics of neural activity via electrical recording relies on the ability to detect and sort neural spikes recorded from a number of neurons by the same electrode. This article reviews methods for detecting and classifying action potentials, a problem commonly referred to as spike sorting.

Comparison Trees: Sorting and Selection

Adaptive Sorting with AVL Trees

A new adaptive sorting algorithm is introduced. The new implementation relies on using the traditional AVL trees, and has the same performance limitations. More precisely, the number of comparisons performed by our algorithm, on an input sequence of length n that has I inversions, is at most 1.44n lg I n + O(n) . Our algorithm runs in time O(n log I n ) and is practically efficient and easy to ...

Using k-d Trees for Robust 3D Point Pattern Matching

We propose a new method for matching two 3D point sets of identical cardinality with global similarity but locally non-rigid distribution. This problem arises from markerbased optical motion capture systems. The point-sets are extracted from similar design poses of two subjects with underlying non-rigidity and possible distribution discrepancies, one being a model set (manually identified) and ...