Algorithm Design
Jon Kleinberg and Eva Tardos

Table of Contents

1 Introduction: Some Representative Problems

1.1 A First Problem: Stable Matching

    1.2 Five Representative Problems
          Solved Exercises
          Excercises
          Notes and Further Reading

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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