Algorithm Design, 1st edition

  • Jon Kleinberg
  • Eva Tardos
  • Éva Tardos

Algorithm Design

ISBN-13:  9780321295354

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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.

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

Table of contents

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
          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  
          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  
          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
          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
          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
            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
            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
        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
         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
             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
             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
             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
               Notes and Further Reading


Epilogue: Algorithms that Run Forever 



Published by Pearson (March 16th 2005) - Copyright © 2006