For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

Randomized Algorithms

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

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Computational Complexity: A Modern Approach

The dominant explanation for the spread of technological innovations emphasizes processes of influence and information flow. Firms which are closely connected to pre-existing users of an innovation learn about it and adopt it early on. Firms at the periphery of communication networks are slower to adopt.

This paper develops an alternative model which emphasizes the role of know-how and organizational learning as potential barriers to adoption of innovations. Firms delay in-house adoption of complex technology until they obtain sufficient technical know-how to implement and operate it successfully.

In response to knowledge barriers, new institutions come into existence which progressively lower those barriers, and make it easier for firms to adopt and use the technology without extensive in-house expertise. Service bureaus, consultants, and simplification of the technology are examples. As knowledge barriers are lowered, diffusion speeds up, and one observes a transition from an early pattern in which the new technology is typically obtained as a service to a later pattern of in-house provision of the technology.

Thus the diffusion of technology is reconceptualized in terms of organizational learning, skill development, and knowledge barriers. The utility of this approach is shown through an empirical study of the diffusion of business computing in the United States, reporting survey and ethnographic data on the spread of business computing, on the learning processes and skills required, and on the changing institutional practices that facilitated diffusion.

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Technology Diffusion and Organizational Learning: The Case of Business Computing

In 1964 Kolmogorov introduced the concept of the complexity of a finite object (for instance, the words in a certain alphabet). He defined complexity as the minimum number of binary signs containing all the information about a given object that are sufficient for its recovery (decoding). This definition depends essentially on the method of decoding. However, by means of the general theory of algorithms, Kolmogorov was able to give an invariant (universal) definition of complexity. Related concepts were investigated by Solomonoff (U.S.A.) and Markov. Using the concept of complexity, Kolmogorov gave definitions of the quantity of information in finite objects and of the concept of a random sequence (which was then defined more precisely by Martin-Lof). Afterwards, this circle of questions developed rapidly. In particular, an interesting development took place of the ideas of Markov on the application of the concept of complexity to the study of quantitative questions in the theory of algorithms. The present article is a survey of the fundamental results connected with the brief remarks above.

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The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms

Computability by Probabilistic Machines

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Toward an ethics and etiquette for electronic mail

: An investigation is made of the degrees of computability (in the theoretical sense) of certain decision problems. The Kleene hierarchy is extended to partial relations. (Author)

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Degrees of computability

Review: E. Mark Gold, Limiting Recursion; Hilary Putnam, Trial and Error Predicates and the Solution to a Problem of Mostowski

E. Mark Gold. Limiting recursion. The journal of symbolic logic , vol. 30 (1965), pp. 28–48. - Hilary Putnam. Trial and error predicates and the solution to a problem of Mostowski. The journal of symbolic logic , vol. 30 (1965), pp. 49–57.

Norman Shapiro

Papers

Computability by Probabilistic Machines

Toward an ethics and etiquette for electronic mail

Degrees of computability

Review: E. Mark Gold, Limiting Recursion; Hilary Putnam, Trial and Error Predicates and the Solution to a Problem of Mostowski

E. Mark Gold. Limiting recursion. The journal of symbolic logic , vol. 30 (1965), pp. 28–48. - Hilary Putnam. Trial and error predicates and the solution to a problem of Mostowski. The journal of symbolic logic , vol. 30 (1965), pp. 49–57.