Algorithm Design

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