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PROBABILISTIC METHODS AND RANDOMIZED
ALGORITHMS
by
Majid Nemati Anaraki
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful¯llment of the
Requirements for the Degree
MASTER OF SCIENCE
(STATISTICS)
May 2007
Copyright 2007 Majid Nemati Anaraki
Object Description
| Title | Probabilistic methods and randomized algorithms |
| Author | Anaraki, Majid Nemati |
| Author email | manemati@gmail.com |
| Degree | Master of Science |
| Document type | Thesis |
| Degree program | Statistics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-03-28 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-04-20 |
| Advisor (committee chair) | Goldstein, Larry |
| Advisor (committee member) |
Baxendale, Peter Sun, Fengzhu |
| Abstract | An algorithm can be defined as a set of computational steps that transform the input to the output. Probabilistic analysis of algorithms is the method of studying how algorithms perform when the input is taken from well defined probabilistic space. In design of algorithms to solve many important problems, randomized algorithms are either the fastest, or the simplest algorithms, and often both.; In this study, different probabilistic methods will be investigated. Useful and well known bounds such as Chernoff bounds and Ramsey theory, first and second moment methods and Lovasz local lemma (LLL) are considered to analyze the algorithmic and combinatorial problems of interest. Pure and accelerated random search algorithms and some of their convergence properties will be considered in the last section.; We'll see that the gains in random algorithms come at a price that the answers may have some positive probability of being incorrect. Although it may seem unusual to design an algorithm that may be incorrect, if the probability of error is sufficiently small then the improvement in speed or memory requirements may well be worthwhile. |
| Keyword | probabilistic methods |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m426 |
| Rights | Anaraki, Majid Nemati |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Anaraki-20070420 |
| Archival file | uscthesesreloadpub_Volume23/etd-Anaraki-20070420.pdf |
Description
| Title | Page 1 |
| Full text | PROBABILISTIC METHODS AND RANDOMIZED ALGORITHMS by Majid Nemati Anaraki A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful¯llment of the Requirements for the Degree MASTER OF SCIENCE (STATISTICS) May 2007 Copyright 2007 Majid Nemati Anaraki |
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