LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur

Sorting, Peers and Achievement of Aboriginal Students in British Columbia

We use administrative data on students in grades 4 and 7 in British Columbia to examine the extent to which differences in school environment contribute to the achievement gap between Aboriginal and non-Aboriginal students as measured by standardized test scores. We find that segregation of Aboriginal and non-Aboriginal students is substantial, and that differences in the distribution of these two groups across schools account for roughly half the overall achievement gap on the Foundation Skills Assessment tests in grade 7. The substantial school-level segregation of Aboriginal and non-Aboriginal student across schools means that Aboriginal students on average have a higher proportion of peers who are themselves Aboriginal, as well as a higher proportion of peers in special education. We estimate the effect of peer composition on value-added exam outcomes, using longitudinal data on multiple cohorts of students together with school-by-grade fixed effects to account for endogenous selection into schools. We find that having a greater proportion of Aboriginal peers, if anything, improves the achievement of Aboriginal students.Aboriginal education, peer effects

Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

Adaptive sorting algorithms for evaluation of automatic zoning

Optical Character Recognition (OCR) involves analysis of machine-printed and hand written document images. The first step in an OCR process is to locate the text to be recognized on a page. An OCR device tries to identify the characters in these text regions and outputs the characters in ASCII. To evaluate the performance of any OCR device, the ASCII output of the OCR device is compared with the ground truth text which is entered into the computer manually; Some OCR devices provide the users with automatic zoning. The output of any automatic zoning algorithm has to be corrected manually to restore the correct reading order. This is done by elementary edit operations such as insertions, deletions and substitutions or by moving sub-strings of characters. The efficiency of an automatic zoning algorithm is measured by the cost of correcting the OCR generated text. The model for cost calculation requires movement of sub-strings in a particular fashion to ensure minimal cost. This problem has been modeled as sorting an arbitrary permutation. This thesis presents few adaptive sorting approaches which can be incorporated into the automatic zoning evaluation algorithm. These algorithms perform better than the existing algorithms used for this purpose. This thesis also presents more directions in which the problem can be pursued to achieve better performance

Does adult ADHD interact with COMT val 158 met genotype to influence working memory performance?

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