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| Preface | |
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| Analysis Basics | |
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| What is Analysis? | |
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| Input Classes | |
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| Space Complexity | |
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| Exercises | |
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| What to Count and Consider | |
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| Cases to Consider | |
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| Exercises | |
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| Mathematical Background | |
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| Logarithms | |
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| Binary Trees | |
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| Probabilities | |
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| Summations | |
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| Exercises | |
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| Rates of Growth | |
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| Classification of Growth | |
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| Exercises | |
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| Divide and Conquer Algorithms | |
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| Tournament Method | |
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| Lower Bounds | |
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| Exercises | |
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| Recurrence Relations | |
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| Exercises | |
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| Analyzing Programs | |
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| Searching and Selection Algorithms | |
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| Sequential Search | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| Binary Search | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| Selection | |
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| Exercises | |
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| Programming Exercise | |
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| Sorting Algorithms | |
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| Insertion Sort | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| Bubble Sort | |
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| Best-Case Analysis | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| Shellsort | |
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| Algorithm Analysis | |
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| The Effect of the Increment | |
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| Exercises | |
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| Radix Sort | |
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| Analysis | |
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| Exercises | |
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| Heapsort | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| Merge Sort | |
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| MergeLists Analysis | |
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| MergeSort Analysis | |
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| Exercises | |
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| Quicksort | |
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| Worst-Case Analysis | |
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| Average-Case Analysis | |
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| Exercises | |
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| External Polyphase Merge Sort | |
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| Number of Comparisons in Run Construction | |
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| Number of Comparisons in Run Merge | |
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| Number of Block Reads | |
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| Exercises | |
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| Additional Exercises | |
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| Programming Exercises | |
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| Numeric Algorithms | |
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| Calculating Polynomials | |
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| Horner's Method | |
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| Preprocessed Coefficients | |
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| Exercises | |
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| Matrix Multiplication | |
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| Winograd's Matrix Multiplication | |
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| Strassen's Matrix Multiplication | |
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| Exercises | |
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| Linear Equations | |
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| Gauss-Jordan Method | |
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| Exercises | |
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| Matching Algorithms | |
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| String Matching | |
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| Finite Automata | |
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| Knuth-Morris-Pratt Algorithm | |
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| Boyer-Moore Algorithm | |
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| Exercises | |
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| Approximate String Matching | |
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| Analysis | |
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| Exercises | |
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| Programming Exercises | |
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| Graph Algorithms | |
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| Graph Background and Terminology | |
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| Terminology | |
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| Exercises | |
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| Data Structure Methods for Graphs | |
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| The Adjacency Matrix | |
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| The Adjacency List | |
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| Exercises | |
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| Depth-First and Breadth-First Traversal Algorithms | |
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| Depth-First Traversal | |
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| Breadth-First Traversal | |
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| Traversal Analysis | |
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| Exercises | |
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| Minimum Spanning Tree Algorithm | |
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| The Dijkstra-Prim Algorithm | |
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| The Kruskal Algorithm | |
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| Exercises | |
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| Shortest-Path Algorithm | |
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| Dijkstra's Algorithm | |
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| Exercises | |
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| Biconnected Component Algorithm | |
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| Exercises | |
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| Partitioning Sets | |
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| Programming Exercises | |
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| Parallel Algorithms | |
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| Parallelism Introduction | |
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| Computer System Categories | |
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| Parallel Architectures | |
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| Principles for Parallelism Analysis | |
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| Exercises | |
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| The PRAM Model | |
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| Exercises | |
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| Simple Parallel Operations | |
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| Broadcasting Data in a CREW PRAM Model | |
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| Broadcasting Data in a EREW PRAM Model | |
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| Finding the Maximum Value in a List | |
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| Exercises | |
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| Parallel Searching | |
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| Exercises | |
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| Parallel Sorting | |
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| Linear Network Sort | |
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| Odd-Even Swap Sort | |
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| Other Parallel Sorts | |
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| Exercises | |
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| Parallel Numerical Algorithms | |
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| Matrix Multiplication on a Parallel Mesh | |
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| Matrix Multiplication in a CRCW PRAM Model | |
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| Solving Systems of Linear Equations with an SIMD Algorithm | |
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| Exercises | |
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| Parallel Graph Algorithms | |
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| Shortest-Path Parallel Algorithm | |
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| Minimum Spanning Tree Parallel Algorithm | |
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| Exercises | |
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| Nondeterministic Algorithms | |
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| What is NP? | |
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| Problem Reductions | |
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| NP-Complete Problems | |
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| Typical NP Problems | |
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| Graph Coloring | |
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| Bin Packing | |
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| Backpack Problem | |
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| Subset Sum Problem | |
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| CNF-Satisfiability Problem | |
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| Job Scheduling Problem | |
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| Exercises | |
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| What Makes Something NP? | |
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| Is P = NP? | |
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| Exercises | |
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| Testing Possible Solutions | |
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| Job Scheduling | |
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| Graph Coloring | |
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| Exercises | |
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| Other Algorithmic Techniques | |
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| Greedy Approximation Algorithms | |
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| Traveling Salesperson Approximations | |
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| Bin Packing Approximations | |
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| Backpack Approximation | |
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| Subset Sum Approximation | |
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| Graph Coloring Approximation | |
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| Exercises | |
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| Probabilistic Algorithms | |
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| Numerical Probabilistic Algorithms | |
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| Monte Carlo Algorithms | |
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| Las Vegas Algorithms | |
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| Sherwood Algorithms | |
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| Probabilistic Algorithm Comparison | |
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| Exercises | |
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| Dynamic Programming | |
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| Array-Based Methods | |
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| Dynamic Matrix Multiplication | |
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| Exercises | |
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| Programming Exercises | |
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| Random Number Table | |
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| Pseudorandom Number Generation | |
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| Results of Chapter Study Suggestion | |
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| References | |
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| Index | |