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Probabilistic Analysis of Algorithms begins with a presentation of the "tools of the trade" currently used in probabilistic analyses, and continues with an applications section in which these tools are used in the analysis ofr selected algorithms. The tools section of the book provides the reader with an arsenal of analytic and numeric computing methods which are then applied to several groups of algorithms to analyze their running time or storage requirements characteristics. Topics covered in the applications section include sorting, communications network protocols and bin packing. While the discussion of the various algorithms is sufficient to motivate their structure, the emphasis throughout is on the probabilistic estimation of their operation under distributional assumptions on their input. Probabilistic Analysis of Algorithms assumes a working knowledge of engineering mathematics, drawing on real and complex analysis, combinatorics and probability theory. While the book is intended primarily as a text for the upper undergraduate and graduate student levels, it contains a wealth of material and should also prove an important reference for researchers. As such it is addressed to computer scientists, mathematicians, operations researchers, and electrical and industrial engineers who are interested in evaluating the probable operation of algorithms, rather than their worst-case behavior.
Table des matières
1 Introduction.- 1.1 Criteria for the Performance and Quality of Algorithms.- 1.2 The Analysis of a Very Simple Algorithm.- 1.3 Comments on Sources and Resources.- 2 Tools of the Trade.- 2.1 Introduction to Asymptotics.- 2.2 Generating Functions.- 2.3 Integral Transforms (it's).- 2.4 Combinatorial Calculus (The Symbolic Operator Method).- 2.5 Asymptotics from Generating Functions.- 2.6 Selected Results from Probability Theory.- 3 Algorithms over Permutations.- 3.1 MAX - Locating the Largest Term in a Permutation.- 3.2 Representations of Permutations.- 3.3 Analysis of Sorting Algorithms.- 4 Algorithms for Communications Networks.- 4.1 The Efficiency of Multiple Connections.- 4.2 Collision Resolution Stack Algorithms.- 5 Bin Packing Heuristics.- 5.1 The Next-Fit Bin Packing Algorithm.- 5.2 The Next-Fit-Decreasing Bin Packing Algorithm.- Appendix A: Binomial Coefficients.- Appendix B: Stirling Numbers.- Appendix C: Inequalities.- References.- Notation Index.
