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Algorithm Design
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Table of Contents

I Fundamental Tools 1 1 Algorithm Analysis 3 1.1 Methodologies for Analyzing Algorithms 5 1.2 Asymptotic Notation 13 1.3 A Quick Mathematical Review 21 1.4 Case Studies in Algorithm Analysis 31 1.5 Amortization 34 1.6 Experimentation 42 1.7 Exercises 47 2 Basic Data Structures 55 2.1 Stack sand Queues 57 2.2 Vectors, Lists, and Sequences 65 2.3 Trees 75 2.4 Priority Queues and Heaps 94 2.5 Dictionaries and Hash Tables 114 2.6 Java Example: Heap 128 2.7 Exercises 131 3 Search Trees and Skip Lists 139 3.1 Ordered Dictionaries and Binary Search Trees 141 3.2 AVL Trees 152 3.3 Bounded-Depth Search Trees 159 3.4 Splay Trees 185 3.5 Sk i p Lists 195 3.6 Java Example: AVL and Red-Black Trees 202 3.7 Exercises 212 4 Sorting, Sets, and Selection 217 4.1 Merge-Sort 219 4.2 The Set Abstract Data Type 225 4.3 Quick -Sort 235 4.4 A Lower Bound on Comparison-Based Sorting 239 4.5 Buck et-Sort and Radix-Sort 241 4.6 Comparison of Sorting Algorithms 244 4.7 Selection 245 4.8 Java Example: In-Place Quick -Sort 248 4.9 Exercises 251 5 Fundamental Techniques 257 5.1 The GreedyMethod 259 5.2 Divide-and-Conquer 263 5.3 Dynamic Programming 274 5.4 Exercises 282 II Graph Algorithms 285 6 Graphs 287 6.1 The Graph Abstract Data Type 289 6.2 Data Structures for Graphs 296 6.3 Graph Traversal 303 6.4 Directed Graphs 316 6.5 Java Example: Depth-First Search 329 6.6 Exercises 335 7 Weighted Graphs 339 7.1 Single-Source Shortest Paths 341 7.2 All-Pairs Shortest Paths 354 7.3 Minimum Spanning Trees 360 7.4 Java Example: Dijk stra's Algorithm 373 7.5 Exercises 376 8 Network Flow and Matching 381 8.1 Flows and Cuts 383 8.2 Maximum Flow 387 8.3 Maximum BipartiteMatching 396 8.4 Minimum-Cost Flow 398 8.5 Java Example: Minimum-Cost Flow 405 8.6 Exercises 412 III Internet Algorithmics 415 9 Text Processing 417 9.1 Strings and PatternMatching Algorithms 419 9.2 Tries 429 9.3 Text Compression 440 9.4 Text Similarity Testing 443 9.5 Exercises 447 10 Number Theory and Cryptography 451 10.1 Fundamental Algorithms Involving Numbers 453 10.2 Cryptographic Computations 471 10.3 Information Security Algorithms and Protocols 481 10.4 The Fast Fourier Transform 488 10.5 Java Example: FFT 500 10.6 Exercises 508 11 Network Algorithms 511 11.1 ComplexityMeasures and Models 513 11.2 Fundamental Distributed Algorithms 517 11.3 Broadcast and Unicast Routing 530 11.4 Multicast Routing 535 11.5 Exercises 541 IV Additional Topics 545 12 Computational Geometry 547 12.1 Range Trees 549 12.2 Priority Search Trees 556 12.3 Quadtrees and k-D Trees 561 12.4 The Plane Sweep Technique 565 12.5 Convex Hulls 572 12.6 Java Example: Convex Hull 583 12.7 Exercises 587 13 NP-Completeness 591 13.1 P and NP 593 13.2 NP-Completeness 599 13.3 Important NP-Complete Problems 603 13.4 Approximation Algorithms 618 13.5 Back track i ng and Branch-and-Bound 627 13.6 Exercises 638 14 Algorithmic Frameworks 643 14.1 External-Memory Algorithms 645 14.2 Parallel Algorithms 657 14.3 Online Algorithms 667 14.4 Exercises 680 A Useful Mathematical Facts 685 Bibliography 689 Index 698

About the Author

Michael T. Goodrich is a mathematician and computer scientist. He is a Chancellor's Professor and the chair of Department of Computer Science, of Donald Bren School of Information and Computer Sciences, a school of University of California, Irvine. Roberto Tamassia is the author of Algorithm Design: Foundations, Analysis, and Internet Examples, published by Wiley.

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