The Algorithm Design Manual

Contents

u Techniques

u Introduction to Algorithms

u Correctness and Efficiency

u Correctness

u Efficiency

u Expressing Algorithms

u Keeping Score

u The RAM Model of Computation

u Best, Worst, and Average-Case Complexity

u The Big Oh Notation

u Growth Rates

u Logarithms

u Modeling the Problem

u About the War Stories

u War Story: Psychic Modeling

u Exercises

u Data Structures and Sorting

u Fundamental Data Types

u Containers

u Dictionaries

u Binary Search Trees

u Priority Queues

u Specialized Data Structures

u Sorting

u Applications of Sorting

u Approaches to Sorting

u Data Structures

u Incremental Insertion

u Divide and Conquer

u Randomization

u Bucketing Techniques

u War Story: Stripping Triangulations

u War Story: Mystery of the Pyramids

u War Story: String 'em Up

u Exercises

u Breaking Problems Down

u Dynamic Programming

u Fibonacci numbers

u The Partition Problem

u Approximate String Matching

u Longest Increasing Sequence

u Minimum Weight Triangulation

u Limitations of Dynamic Programming

u War Story: Evolution of the Lobster

u War Story: What's Past is Prolog

u War Story: Text Compression for Bar Codes

u Divide and Conquer

u Fast Exponentiation

u Binary Search

u Square and Other Roots

u Exercises

u Graph Algorithms

u The Friendship Graph

u Data Structures for Graphs

u War Story: Getting the Graph

u Traversing a Graph

u Breadth-First Search

u Depth-First Search

u Applications of Graph Traversal

u Connected Components

u Tree and Cycle Detection

u Two-Coloring Graphs

u Topological Sorting

u Articulation Vertices

u Modeling Graph Problems

u Minimum Spanning Trees

u Prim's Algorithm

u Kruskal's Algorithm

u Shortest Paths

u Dijkstra's Algorithm

u All-Pairs Shortest Path

u War Story: Nothing but Nets

u War Story: Dialing for Documents

u Exercises

u Combinatorial Search and Heuristic Methods

u Backtracking

u Constructing All Subsets

u Constructing All Permutations

u Constructing All Paths in a Graph

u Search Pruning

u Bandwidth Minimization

u War Story: Covering Chessboards

u Heuristic Methods

u Simulated Annealing

u Traveling Salesman Problem

u Maximum Cut

u Independent Set

u Circuit Board Placement

u Neural Networks

u Genetic Algorithms

u War Story: Annealing Arrays

u Parallel Algorithms

u War Story: Going Nowhere Fast

u Exercises

u Intractable Problems and Approximations

u Problems and Reductions

u Simple Reductions

u Hamiltonian Cycles

u Independent Set and Vertex Cover

u Clique and Independent Set

u Satisfiability

u The Theory of NP-Completeness

u 3-Satisfiability

u Difficult Reductions

u Integer Programming

u Vertex Cover

u Other NP-Complete Problems

u The Art of Proving Hardness

u War Story: Hard Against the Clock

u Approximation Algorithms

u Approximating Vertex Cover

u The Euclidean Traveling Salesman

u Exercises

u How to Design Algorithms

u Resources

u A Catalog of Algorithmic Problems

u Data Structures

u Dictionaries

u Priority Queues

u Suffix Trees and Arrays

u Graph Data Structures

u Set Data Structures

u Kd-Trees

u Numerical Problems

u Solving Linear Equations

u Bandwidth Reduction

u Matrix Multiplication

u Determinants and Permanents

u Constrained and Unconstrained Optimization

u Linear Programming

u Random Number Generation

u Factoring and Primality Testing

u Arbitrary-Precision Arithmetic

u Knapsack Problem

u Discrete Fourier Transform

u Combinatorial Problems

u Sorting

u Searching

u Median and Selection

u Generating Permutations

u Generating Subsets

u Generating Partitions

u Generating Graphs

u Calendrical Calculations

u Job Scheduling

u Satisfiability

u Graph Problems: Polynomial-Time

u Connected Components

u Topological Sorting

u Minimum Spanning Tree

u Shortest Path

u Transitive Closure and Reduction

u Matching

u Eulerian Cycle / Chinese Postman

u Edge and Vertex Connectivity

u Network Flow

u Drawing Graphs Nicely

u Drawing Trees

u Planarity Detection and Embedding

u Graph Problems: Hard Problems

u Clique

u Independent Set

u Vertex Cover

u Traveling Salesman Problem

u Hamiltonian Cycle

u Graph Partition

u Vertex Coloring

u Edge Coloring

u Graph Isomorphism

u Steiner Tree

u Feedback Edge/Vertex Set

u Computational Geometry

u Robust Geometric Primitives

u Convex Hull

u Triangulation

u Voronoi Diagrams

u Nearest Neighbor Search

u Range Search

u Point Location

u Intersection Detection

u Bin Packing

u Medial-Axis Transformation

u Polygon Partitioning

u Simplifying Polygons

u Shape Similarity

u Motion Planning

u Maintaining Line Arrangements

u Minkowski Sum

u Set and String Problems

u Set Cover

u Set Packing

u String Matching

u Approximate String Matching

u Text Compression

u Cryptography

u Finite State Machine Minimization

u Longest Common Substring

u Shortest Common Superstring

u Algorithmic Resources

u Software systems

u LEDA

u Netlib

u Collected Algorithms of the ACM

u The Stanford GraphBase

u Combinatorica

u Algorithm Animations with XTango

u Programs from Books

u Discrete Optimization Algorithms in Pascal

u Handbook of Data Structures and Algorithms

u Combinatorial Algorithms for Computers and Calculators

u Algorithms from P to NP

u Computational Geometry in C

u Algorithms in C++

u Data Sources

u Textbooks

u On-Line Resources

u Literature

u People

u Software

u Professional Consulting Services

u References

u Index

u About this document ...

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