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Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, balls and bins models, the probabilistic method, and Markov chains. In the second half, the authors delve into more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods, coupling, martingales, and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Computer science --- Algorithms --- Probabilities --- Stochastic analysis --- Algorithmes --- Probabilités --- Analyse stochastique --- Algorithms. --- Probabilities. --- Stochastic analysis. --- Probabilités --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Algorism --- Algebra --- Arithmetic --- Foundations
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"Greatly expanded, this new edition requires only an elementary background in discrete mathematics and offers a comprehensive introduction to the role of randomization and probabilistic techniques in modern computer science. Newly added chapters and sections cover topics including normal distributions, sample complexity, VC dimension, Rademacher complexity, power laws and related distributions, cuckoo hashing, and the Lovasz Local Lemma. Material relevant to machine learning and big data analysis enables students to learn modern techniques and applications. Among the many new exercises and examples are programming-related exercises that provide students with excellent training in solving relevant problems. This book provides an indispensable teaching tool to accompany a one- or two-semester course for advanced undergraduate students in computer science and applied mathematics"--
Algorithms. --- Probabilities. --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Algorism --- Algebra --- Arithmetic --- Foundations --- Algorithmes --- Probabilités --- Analyse stochastique --- Algorithms --- Probabilities --- Stochastic analysis --- 510.5 --- 510.5 Algorithms. Computable functions --- Algorithms. Computable functions --- Probabilités --- Computer science
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Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
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This book constitutes the refereed proceedings of the 10th International Workshop on Algorithms and Models for the Web Graph, WAW 2013, held in Cambridge, MA, USA, in December 2013. The 17 papers presented were carefully reviewed and selected for inclusion in this volume. They address topics related to graph-theoretic and algorithmic aspects of related complex networks, including citation networks, social networks, biological networks, molecular networks and other networks arising from the Internet.
Computer science. --- Computer software. --- Computational complexity. --- Data mining. --- Information storage and retrieval systems. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Data Mining and Knowledge Discovery. --- Information Storage and Retrieval. --- Engineering & Applied Sciences --- Computer Science --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Complexity, Computational --- Informatics --- Software, Computer --- Algorithms. --- Computer science --- Information storage and retrieval. --- Mathematics. --- Computer algorithms --- Data mining --- Information storage and retrieva. --- Database searching --- Electronic data processing --- Machine theory --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval --- Computer science—Mathematics. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Discrete mathematics. --- Data centers --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis
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This book constitutes the refereed proceedings of the 10th International Workshop on Algorithms and Models for the Web Graph, WAW 2013, held in Cambridge, MA, USA, in December 2013. The 17 papers presented were carefully reviewed and selected for inclusion in this volume. They address topics related to graph-theoretic and algorithmic aspects of related complex networks, including citation networks, social networks, biological networks, molecular networks and other networks arising from the Internet.
Information retrieval --- Complex analysis --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- Information systems --- Computer. Automation --- IR (information retrieval) --- complexiteit --- discrete wiskunde --- complexe analyse (wiskunde) --- bedrijfssoftware --- computers --- informatica --- informatiesystemen --- database management --- computerkunde --- moleculaire biologie --- data acquisition
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