1 Models of Computation 1.1 Algorithms and their complexity 1.2 Random access machines 1.3 Computational complexity of RAM programs 1.4 A stored program model 1.5 Abstractions of the RAM 1.6 A primitive model of computation: the Turing machine 1.7 Relationship between the Turing machine and RAM models 1.8 Pidgin ALGOL-a high-level language 2 Design of Efficient Algorithms 2.1 Data structures: lists, queues, and stacks 2.2 Set representations 2.3 Graphs 2.4 Trees 2.5 Recursion 2.6 Divide-and-conquer 2.7 Balancing 2.8 Dynamic programming 2.9 Epilogue 3 Sorting and Order Statistics 3.1 The sorting problem 3.2 Radix sorting 3.3 Sorting by comparisons 3.4 Heapsort-an O(n log n) comparison sort 3.5 Quicksort-an O(n log n) expected time sort 3.6 Order statistics 3.7 Expected time for order statistics 4 Data Structures for Set Manipulation Problems 4.1 Fundamental operations on sets 4.2 Hashing 4.3 Binary search 4.4 Binary search trees 4.5 Optimal binary search trees 4.6 A simple disjoint-set union algorithm 4.7 Tree structures for the UNION-FIND problem 4.8 Applications and extensions of the UNION-FIND algorithm 4.9 Balanced tree schemes 4.10 Dictionaries and priority queues 4.11 Mergeable heaps 4.12 Concatenable queues 4.13 Partitioning 4.14 Chapter summary 5 Algorithms on Graphs 5.1 Minimum-cost spanning trees 5.2 Depth-first search 5.3 Biconnectivity 5.4 Depth-first search of a directed graph 5.5 Strong connectivity 5.6 Path-finding problems 5.7 A transitive closure algorithm 5.8 A shortest-path algorithm 5.9 Path problems and matrix multiplication 5.10 Single-source problems 5.11 Dominators in a directed acyclic graph: putting the concepts together. 6 Matrix Multiplication and Related Operations 6.1 Basics 6.2 Strassen's matrix-multiplication algorithm 6.3 Inversion of matrices 6.4 LU P decomposition of matrices 6.5 Applications of LUP decomposition 6.6 Boolean matrix multiplication 7 The Fast Fourier Transform and its Applications 7.1 The discrete Fourier transform and its inverse 7.2 The fast Fourier transform algorithm 7.3 The FFT using bit operations 7.4 Products of polynomials 7.5 The Schonhage-Strassen integer-multiplication algorithm 8 Integer and Polynomial Arithmetic 8.1 The similarity between integers and polynomials 8.2 Integer multiplication and division 8.3 Polynomial multiplication and division 8.4 Modular arithmetic 8.5 Modular polynomial arithmetic and polynomial evaluation. 8.6 Chinese remaindering 8.7 Chinese remaindering and interpolation of polynomials... 8.8 Greatest common divisors and Euclid's algorithm 8.9 An asymptotically fast algorithm for polynomial GCD's.. 8.10 Integer GCD's 8.11 Chinese remaindering revisited 8.12 Sparse polynomials 9 Pattern-Matching Algorithms 9.1 Finite automata and regular expressions 9.2 Recognition of regular expression patterns 9.3 Recognition of substrings 9.4 Two-way deterministic pushdown automata 9.5 Position trees and substring identifiers 10 NP.Complete Problems 10.1 Noncleterministic Turing machines 10.2 The classes and 10.3 Languages and problems 10.4 NP-completeness of the satisfiability problem 10.5 Additional NP-complete problems 10.6 Polynomial-space-bounded problems 11 Some Provably Intractable Problems 11.1 Complexity hierarchies 11.2. The space hierarchy for deterministic Turing machines 11.3 A problem requiring exponential time and space 11.4 A nonelementary problem
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