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# Algorithm Design, 1st edition

Published by Pearson (March 16, 2005) © 2006

**Jon Kleinberg**Cornell University**Eva Tardos**Cornell University

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August 6, 2009 **Author, Jon Kleinberg, was recently cited in the New York Times for his statistical analysis research in the Internet age.**

**Algorithm Design **introduces algorithms by looking at the real-world problems that motivate them. The book teaches students a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science.

- Focus on problem analysis and design techniques.
- Discussion is grounded in concrete problems and examples rather than abstract presentation of principles, with representative problems woven throughout the text.
- Over 200 well crafted problems from companies such as Yahoo!
^{®}and Oracle^{®}. Each problem has been class tested for usefulness and accuracy in the authors' own undergraduate algorithms courses. - Broad coverage of algorithms for dealing with NP-hard problems and the application of randomization, increasingly important topics in algorithms.

## Table of Contents

Algorithm Design

Jon Kleinberg and Eva Tardos

- Introduction: Some Representative Problems
- 1.1 A First Problem: Stable Matching
- 1.2 Five Representative Problems

- Solved Exercises
- Excercises
- Notes and Further Reading

- Basics of Algorithms Analysis
- 2.1 Computational Tractability
- 2.2 Asymptotic Order of Growth Notation
- 2.3 Implementing the Stable Matching Algorithm using Lists and Arrays
- 2.4 A Survey of Common Running Times
- 2.5 A More Complex Data Structure: Priority Queues

- Solved Exercises
- Exercises
- Notes and Further Reading

- Graphs
- 3.1 Basic Definitions and Applications
- 3.2 Graph Connectivity and Graph Traversal
- 3.3 Implementing Graph Traversal using Queues and Stacks
- 3.4 Testing Bipartiteness: An Application of Breadth-First Search
- 3.5 Connectivity in Directed Graphs
- 3.6 Directed Acyclic Graphs and Topological Ordering

- Solved Exercises
- Exercises
- Notes and Further Reading

- Greedy Algorithms
- 4.1 Interval Scheduling: The Greedy Algorithm Stays Ahead
- 4.2 Scheduling to Minimize Lateness: An Exchange Argument
- 4.3 Optimal Caching: A More Complex Exchange Argument
- 4.4 Shortest Paths in a Graph
- 4.5 The Minimum Spanning Tree Problem
- 4.6 Implementing Kruskal's Algorithm: The Union-Find Data Structure
- 4.7 Clustering
- 4.8 Huffman Codes and the Problem of Data Compression
- *4.9 Minimum-Cost Arborescences: A Multi-Phase Greedy Algorithm

- Solved Exercises
- Excercises
- Notes and Further Reading

- Divide and Conquer
- 5.1 A First Recurrence: The Mergesort Algorithm
- 5.2 Further Recurrence Relations
- 5.3 Counting Inversions
- 5.4 Finding the Closest Pair of Points
- 5.5 Integer Multiplication
- 5.6 Convolutions and The Fast Fourier Transform

- Solved Exercises
- Exercises
- Notes and Further Reading

- Dynamic Programming
- 6.1 Weighted Interval Scheduling: A Recursive Procedure
- 6.2 Weighted Interval Scheduling: Iterating over Sub-Problems
- 6.3 Segmented Least Squares: Multi-way Choices
- 6.4 Subset Sums and Knapsacks: Adding a Variable
- 6.5 RNA Secondary Structure: Dynamic Programming Over Intervals
- 6.6 Sequence Alignment
- 6.7 Sequence Alignment in Linear Space
- 6.8 Shortest Paths in a Graph
- 6.9 Shortest Paths and Distance Vector Protocols
- *6.10 Negative Cycles in a Graph

- Solved Exercises
- Exercises
- Notes and Further Reading

- Network Flow
- 7.1 The Maximum Flow Problem and the Ford-Fulkerson Algorithm
- 7.2 Maximum Flows and Minimum Cuts in a Network
- 7.3 Choosing Good Augmenting Paths
- *7.4 The Preflow-Push Maximum Flow Algorithm
- 7.5 A First Application: The Bipartite Matching Problem
- 7.6 Disjoint Paths in Directed and Undirected Graphs
- 7.7 Extensions to the Maximum Flow Problem
- 7.8 Survey Design
- 7.9 Airline Scheduling
- 7.10 Image Segmentation
- 7.11 Project Selection
- 7.12 Baseball Elimination
- *7.13 A Further Direction: Adding Costs to the Matching Problem

- Solved Exercises
- Exercises
- Notes and Further Reading

- NP and Computational Intractability
- 8.1 Polynomial-Time Reductions
- 8.2 Reductions via "Gadgets": The Satisfiability Problem
- 8.3 Efficient Certification and the Definition of NP
- 8.4 NP-Complete Problems
- 8.5 Sequencing Problems
- 8.6 Partitioning Problems
- 8.7 Graph Coloring
- 8.8 Numerical Problems
- 8.9 Co-NP and the Asymmetry of NP
- 8.10 A Partial Taxonomy of Hard Problems

- Solved Exercises
- Exercises
- Notes and Further Reading

- PSPACE: A Class of Problems Beyond NP
- 9.1 PSPACE
- 9.2 Some Hard Problems in PSPACE
- 9.3 Solving Quantified Problems and Games in Polynomial Space
- 9.4 Solving the Planning Problem in Polynomial Space
- 9.5 Proving Problems PSPACE-Complete

- Solved Exercises
- Exercises
- Notes and Further Reading

- Extending the Limits of Tractability
- 10.1 Finding Small Vertex Covers
- 10.2 Solving NP-Hard Problem on Trees
- 10.3 Coloring a Set of Circular Arcs
- *10.4 Tree Decompositions of Graphs
- *10.5 Constructing a Tree Decomposition

- Solved Exercises
- Exercises
- Notes and Further Reading

- Approximation Algorithms
- 11.1 Greedy Algorithms and Bounds on the Optimum: A Load Balancing Problem
- 11.2 The Center Selection Problem
- 11.3 Set Cover: A General Greedy Heuristic
- 11.4 The Pricing Method: Vertex Cover
- 11.5 Maximization via the Pricing method: The Disjoint Paths Problem
- 11.6 Linear Programming and Rounding: An Application to Vertex Cover
- *11.7 Load Balancing Revisited: A More Advanced LP Application
- 11.8 Arbitrarily Good Approximations: the Knapsack Problem

- Solved Exercises
- Exercises
- Notes and Further Reading

- Local Search
- 12.1 The Landscape of an Optimization Problem
- 12.2 The Metropolis Algorithm and Simulated Annealing
- 12.3 An Application of Local Search to Hopfield Neural Networks
- 12.4 Maximum Cut Approximation via Local Search
- 12.5 Choosing a Neighbor Relation
- *12.6 Classification via Local Search
- 12.7 Best-Response Dynamics and Nash Equilibria

- Solved Exercises
- Exercises
- Notes and Further Reading

- Randomized Algorithms
- 13.1 A First Application: Contention Resolution
- 13.2 Finding the Global Minimum Cut
- 13.3 Random Variables and their Expectations
- 13.4 A Randomized Approximation Algorithm for MAX 3-SAT
- 13.5 Randomized Divide-and-Conquer: Median-Finding and Quicksort
- 13.6 Hashing: A Randomized Implementation of Dictionaries
- 13.7 Finding the Closest Pair of Points: A Randomized Approach
- 13.8 Randomized Caching
- 13.9 Chernoff Bounds
- 13.10 Load Balancing
- *13.11 Packet Routing
- 13.12 Background: Some Basic Probability Definitions

- Solved Exercises
- Exercises
- Notes and Further Reading

#### Epilogue: Algorithms that Run Forever

#### References

#### Index

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