Polyteknisk Boghandel

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.

Algorithm Design Jon Kleinberg and Eva Tardos Table of Contents 1 Introduction: Some Representative Problems1. 1A First Problem: Stable Matching1. 2Five Representative Problems Solved Exercises Excercises Notes and Further Reading2 Basics of Algorithms Analysis2.
1 Computational Tractability2.
2 Asymptotic Order of Growth Notation2.
3 Implementing the Stable Matching Algorithm using Lists and Arrays2.
4 A Survey of Common Running Times2.
5 A More Complex Data Structure: Priority QueuesSolved Exercises Exercises Notes and Further Reading3 Graphs3.
1 Basic Definitions and Applications3.
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 Reading4 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 Reading5 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 Reading6 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 GraphSolved Exercises Exercises Notes and Further Reading7 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. 13A Further Direction: Adding Costs to the Matching Problem Solved Exercises Exercises Notes and Further Reading8 NP and Computational Intractability
8.
1 Polynomial-Time Reductions8.
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 Reading9 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 S