Algorithmics of nonuniformity: tools and paradigms/ Micha Hofri and Hosma Mahmoud

includes Index

Introduction -- Counting -- Symbolic Calculus -- Languages and their generating functions -- Probability in algorithmics -- Functional transforms -- Nonuniform polya urn schemes -- Nonuniform data models -- Sorting Nonuniform Data -- Recursive trees -- Series-parallel graphs

The book focuses a solid presentation about the analysis of algorithms, and the data structures that support them.
Traditionally, algorithmics have been approached either via a probabilistic view or an analytic approach. The authors adopt both approaches and bring them together to get the best of both worlds and benefit from the advantage of each approach. The text examines algorithms that are designed to handle general data—sort any array, find the median of any numerical set, and identify patterns in any setting. At the same time, it evaluates "average" performance, "typical" behavior, or in mathematical terms, the expectations of the random variables that describe their operations. Many exercises are presented, which are essential since they convey additional material complementing the content of the chapters. For this reason, the solutions are more than mere answers, but explain and expand upon related concepts, and motivate further work by the reader.