The Algorithm Design Manual

Transcription

1 Steven S. Skiena The Algorithm Design Manual With 72 Figures Includes CD-ROM THE ELECTRONIC LIBRARY OF SCIENCE

2 Contents Preface vii I TECHNIQUES Introduction to Algorithms Correctness and Efficiency Correctness Efficiency Expressing Algorithms Keeping Score The RAM Model of Computation Best, Worst, and Average-Case Complexity The Big Oh Notation Growth Rates Logarithms Modeling the Problem About the War Stories War Story: Psychic Modeling Exercises Data Structures and Sorting Fundamental Data Types Containers Dictionaries Binary Search Trees Priority Queues Specialized Data Structures Sorting Applications of Sorting

3 Approaches to Sorting Data Structures Incremental Insertion Divide and Conquer Randomization Bucketing Techniques War Story: Stripping Triangulations War Story: Mystery of the Pyramids War Story: String 'em Up Exercises Breaking Problems Down Dynamic Programming Fibonacci numbers The Partition Problem Approximate String Matching Longest Increasing Sequence Minimum Weight Triangulation Limitations of Dynamic Programming War Story: Evolution of the Lobster War Story: What's Past Is Prolog War Story: Text Compression for Bar Codes Divide and Conquer Fast Exponentiation Binary Search Square and Other Roots Exercises Graph Algorithms The Friendship Graph Data Structures for Graphs War Story: Getting the Graph Traversing a Graph Breadth-First Search Depth-First Search Applications of Graph Traversal Connected Components Tree and Cycle Detection Two-Coloring Graphs Topological Sorting Articulation Vertices

4 Contents xiii 4.6 Modeling Graph Problems Minimum Spanning Trees Prim's Algorithm Kruskal's Algorithm Shortest Paths Dijkstra's Algorithm All-Pairs Shortest Path War Story: Nothing but Nets War Story: Dialing for Documents Exercises Combinatorial Search and Heuristic Methods Backtracking Constructing All Subsets Constructing All Permutations Constructing All Paths in a Graph Search Pruning Bandwidth Minimization War Story: Covering Chessboards Heuristic Methods Simulated Annealing Neural Networks Genetic Algorithms War Story: Annealing Arrays Parallel Algorithms War Story: Going Nowhere Fast Exercises Intractable Problems and Approximations Problems and Reductions Simple Reductions Hamiltonian Cycle Independent Set and Vertex Cover Clique and Independent Set Satisfiability The Theory of NP-Completeness Satisfiability Difficult Reductions Integer Programming Vertex Cover 149

5 5 Other NP-Complete Problems The Art of Proving Hardness War Story: Hard Against the Clock Approximation Algorithms Approximating Vertex Cover The Euclidean Traveling Salesman Exercises How to Design Algorithms 163 II RESOURCES 8 A Catalog of Algorithmic Problems Data Structures Dictionaries Priority Queues Suffix Trees and Arrays Graph Data Structures Set Data Structures Kd-Trees Numerical Problems Solving Linear Equations Bandwidth Reduction Matrix Multiplication Determinants and Permanents Constrained and Unconstrained Optimization Linear Programming Random Number Generation Factoring and Primality Testing Arbitrary-Precision Arithmetic Knapsack Problem Discrete Fourier Transform Combinatorial Problems Sorting Searching Median and Selection Generating Permutations Generating Subsets Generating Partitions Generating Graphs Calendrical Calculations fob Scheduling Satisfiability 266

6 Contents xv 8.4 Graph Graph Problems: Polynomial-Time Connected Components Topological Sorting Minimum Spanning Tree Shortest Path Transitive Closure and Reduction Matching Eulerian Cycle / Chinese Postman Edge and Vertex Connectivity Network Flow Drawing Graphs Nicely Drawing Trees Planarity Detection and Embedding Problems: Hard Problems Clique Independent Set Vertex Cover Traveling Salesman Problem Hamiltonian Cycle Graph Partition Vertex Coloring Edge Coloring Graph Isomorphism Steiner Tree Feedback Edge/Vertex Set 8.6 Computational Geometry Robust Geometric Primitives Convex Hull Triangulation Voronoi Diagrams Nearest Neighbor Search Range Search Point Location Intersection Detection Bin Packing Medial-Axis Transformation Polygon Partitioning Simplifying Polygons Shape Similarity Motion Planning Maintaining Line Arrangements Minkowski Sum 8.7 Set and String Problems Set Cover Set Packing

7 8.7.3 String Matching Approximate String Matching Text Compression Cryptography Finite State Machine Minimization Longest Common Substring Shortest Common Superstring Algorithmic Resources Software Systems LEDA Netlib The Stanford GraphBase Combinatorica Algorithm Animations with XTango Programs from Books Data Sources Textbooks On-Line Resources Literature People Software Professional Consulting Services 437 Bibliography 439 Index 463