Computing For Life Sciences
Computing For Life Sciences CS 59000
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This 9 page Class Notes was uploaded by Nick Rowe on Saturday September 19, 2015. The Class Notes belongs to CS 59000 at Purdue University taught by Pandurangan in Fall. Since its upload, it has received 55 views. For similar materials see /class/208049/cs-59000-purdue-university in ComputerScienence at Purdue University.
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Date Created: 09/19/15
C5590R Randomized Algorithms and Probabilistic Techniques in CS Gopal Pandurangan gopal cspurdueedu Office C8128 webpage wwwcspurdueeduhomesgopac55902005 newsgroup purduecassc5590r CSSQOR Fall 2005 G Pandurangan Purdue University It is remarkable that this science which originated in the consideration of games and chances should have become the most important object of human knowledge The most important questions of life are for the most part really only problems of probability Pierre Simons Marquis de Laplace 1749 1827 CS590R Fall 2005 G Pandurangan Purdue University 1 Randomization and Computing If somebody would ask me what in the last 10 years what was the most important change in the study of algorithms I would have to say that people getting really familiar with randomized algorithms had to be the winner Donald Knuth Randomization and Religion 1999 CS590R Fall 2005 G Pandurangan Purdue University 2 Probability and Computing 0 Randomized algorithms random steps help 0 Probabilistic analysis of algorithms Why hard problems are sometimes easy to solve in practice 0 Probabilistic deduction statistical inference machine learning Applications Communication networks Cryptography Search engines Fast data structures Scheduling Optimization algorithms Simulation and Modeling Al reasoning Learning Bioinformatics Quantum Computing Complexity Theory CS590R Fall 2005 G Pandurangan Purdue University 3 Topics Theme Emphasis on Probabilistic techniques illustrated by various applications 1 Introduction to probability theory Expectation Linearity of Expectation Moments Variance Deviation bounds Markov Chebyshev and ChernofF Bounds 2 Introduction to Randomized Algorithms and Probabilistic Analysis Las Vegas and Monte Carlo Algorithms Fingerprinting technique Pattern Matching Randomized Quicksort Randomized Selection Stable Marriage Problem Packet Routing 3 Balls and Bins Paradigm Birthday Paradox Coupon Collector39s Problem Poisson Approximation Hashing applications Two choices paradigm CS590R Fall 2005 G Pandurangan Purdue University 4 4 Randomized Graph Algorithms Karger39s Min Cut Algorithm Linear time Minimum Spanning Tree Algorithm Shortest Paths 5 Random walks and Markov chains Markov Chain Basics 2SAT and 3 SAT algorithms Random Walks on Graphs and Undirected Connectivity Variation Distance and Mixing Time Expander Graphs Coupling and Convergence Algorithmic Applications 6 The Probabilistic Method Counting and Expectation techniques Applications Second Moment Method Lovasz Local Lemma Algorithmic application ofthe Lovasz Local Lemma 7 Martingales Introduction Azuma39s Inequality Applications of Azuma39s Inequality 8 Random Graphs CS590R Fall 2005 G Pandurangan Purdue University 5 Models of Random Graphs Threshold Phenomena Connectivity and Giant Component Random Graph Algorithms 9 Online Algorithms Competitive Analysis Caching problem kserver problem 10 Parallel and Distributed Algorithms Sorting on a PRAM Parallel Connectivity Maximal lndependent Set Luby39s algorithm Distributed Dominating Set Problem Contention Resolution Protocols CS590R Fall 2005 G Pandurangan Purdue University 6 References 0 Probability and Computing by M Mitzenmacher and E Upfal o Randomized Algorithms by R Motwani and P Raghavan Probabilistic Method by Alon and Spencer 0 A First Course in Probability by S Ross useful reference for probability Probability and Random Processes by G Grimmett and D Stirzaker reference for more advanced concepts in probability All books are on reserve in the Math Sciences library CS590R Fall 2005 G Pandurangan Purdue University 7 Grading Homeworks 4 or 5 assignments Individually written in Latex Concise and correct proofs Work must be submitted on time Research Project Class Participation Academic Dishonesty policy All submitted work should be on your own Copying or using other people39s work including from the Web or using unauthorized material the reference books listed above are the only authorized material allowed will result in MAX points where MAX is the maximum possible number of points for that assignmentproblemsquiz Repeat offense will result in getting a failure grade in the course and reporting to the Dean of students CS590R Fall 2005 G Pandurangan Purdue University 8