Russ Bubley Knihy

Randomized Algorithms discusses two problems of fine counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.

The book explores the fascinating world of randomized algorithms, which leverage randomness to solve computational problems more efficiently than deterministic methods. It covers fundamental concepts, techniques, and applications, providing a comprehensive overview of how randomness can simplify complex algorithms in areas such as optimization, data structures, and network design. Through detailed examples and theoretical insights, readers gain an understanding of both the power and limitations of these innovative algorithms, making it a valuable resource for computer scientists and mathematicians alike.