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 Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems eBook

Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems


eBook Publisher: John Wiley & Sons
Imprint: Wiley-IEEE Press

Format: Adobe Encrypted (DRM)


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Discover the benefits of applying algorithms to solve scientific, engineering, and practical problems

Providing a combination of theory, algorithms, and simulations, Handbook of Applied Algorithms presents an all-encompassing treatment of applying algorithms and discrete mathematics to practical problems in "hot" application areas, such as computational biology, computational chemistry, wireless networks, and computer vision.

In eighteen self-contained chapters, this timely book explores:
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Localized algorithms that can be used in topology control for wireless ad-hoc or sensor networks
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Bioinformatics algorithms for analyzing data
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Clustering algorithms and identification of association rules in data mining
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Applications of combinatorial algorithms and graph theory in chemistry and molecular biology
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Optimizing the frequency planning of a GSM network using evolutionary algorithms
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Algorithmic solutions and advances achieved through game theory

Complete with exercises for readers to measure their comprehension of the material presented, Handbook of Applied Algorithms is a much-needed resource for researchers, practitioners, and students within computer science, life science, and engineering.

Amiya Nayak, PhD, has over seventeen years of industrial experience and is Full Professor at the School of Information Technology and Engineering at the University of Ottawa, Canada. He is on the editorial board of several journals. Dr. Nayak's research interests are in the areas of fault tolerance, distributed systems/algorithms, and mobile ad-hoc networks. Ivan StojmenoviC?, PhD, is Professor at the University of Ottawa, Canada (www.site.uottawa.ca/~ivan), and Chair Professor of Applied Computing at the University of Birmingham, United Kingdom. Dr. Stojmenovic? received the Royal Society Wolfson Research Merit Award. His current research interests are mostly in the design and analysis of algorithms for wireless ad-hoc and sensor networks.

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Title of Computers eBook: Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems
Release Date: 11-09-2007
Publisher: Wiley-IEEE Press

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Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems


Chapter One

Generating All and Random Instances of a Combinatorial Object

IVAN STOJMENOVIC

1.1 LISTING ALL INSTANCES OF A COMBINATORIAL OBJECT

The design of algorithms to generate combinatorial objects has long fascinated mathematicians and computer scientists. Some of the earliest papers on the interplay between mathematics and computer science are devoted to combinatorial algorithms. Because of its many applications in science and engineering, the subject continues to receive much attention. In general, a list of all combinatorial objects of a given type might be used to search for a counterexample to some conjecture, or to test and analyze an algorithm for its correctness or computational complexity.

This branch of computer science can be defined as follows: Given a combinatorial object, design an efficient algorithm for generating all instances of that object. For example, an algorithm may be sought to generate all n-permutations. Other combinatorial objects include combinations, derangements, partitions, variations, trees, and so on.

When analyzing the efficiency of an algorithm, we distinguish between the cost of generating and cost of listing all instances of a combinatorial object. By generating we mean producing all instances of a combinatorial object, without actually outputting them. Some properties of objects can be tested dynamically, without the need to check each element of a new instance. In case of listing, the output of each object is required. The lower bound for producing all instances of a combinatorial object depends on whether generating or listing is required. In the case of generating, the

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