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Cormen - Introduction to Algorithms (3º Ed) - EXCLUSIVO


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No sé si corresponde a esta sección al no haber lugar para libros de informatica, en tal caso mis disculpas :)

 

 

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Año: 2009

Autores: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein

Paginas: 1313

Formato: pdf

 

 

Table of Contents

Contents

Preface

 

I Foundations

* 1 The Role of Algorithms in Computing

o 1.1 Algorithms

o 1.2 Algorithms as a technology

o Problems

o Chapter notes

* 2 Getting Started

o 2.1 Insertion sort

o 2.2 Analyzing algorithms

o 2.3 Designing algorithms

o Problems

o Chapter notes

* 3 Growth of Functions

o 3.1 Asymptotic notation

o 3.2 Standard notations and common functions

o Problems

o Chapter notes

* 4 Divide-and-Conquer

o 4.1 The maximum-subarray problem

o 4.2 Strassen’s algorithm for matrix multiplication

o 4.3 The substitution method for solving recurrences

o 4.4 The recursion-tree method for solving recurrences

o 4.5 The master method for solving recurrences

o 4.6 Proof of the master theorem

o Problems

o Chapter notes

* 5 Probabilistic Analysis and Randomized Algorithms

o 5.1 The hiring problem

o 5.2 Indicator random variables

o 5.3 Randomized algorithms

o 5.4 Probabilistic analysis and further uses of indicator random variables

o Problems

o Chapter notes

 

II Sorting and Order Statistics

* 6 Heapsort

o 6.1 Heaps

o 6.2 Maintaining the heap property

o 6.3 Building a heap

o 6.4 The heapsort algorithm

o 6.5 Priority queues

o Problems

o Chapter notes

* 7 Quicksort

o 7.1 Description of quicksort

o 7.2 Performance of quicksort

o 7.3 A randomized version of quicksort

o 7.4 Analysis of quicksort

o Problems

o Chapter notes

* 8 Sorting in Linear Time

o 8.1 Lower bounds for sorting

o 8.2 Counting sort

o 8.3 Radix sort

o 8.4 Bucket sort

o Problems

o Chapter notes

* 9 Medians and Order Statistics

o 9.1 Minimum and maximum

o 9.2 Selection in expected linear time

o 9.3 Selection in worst-case linear time

o Problems

o Chapter notes

 

III Data Structures

* 10 Elementary Data Structures

o 10.1 Stacks and queues

o 10.2 Linked lists

o 10.3 Implementing pointers and objects

o 10.4 Representing rooted trees

o Problems

o Chapter notes

* 11 Hash Tables

o 11.1 Direct-address tables

o 11.2 Hash tables

o 11.3 Hash functions

o 11.4 Open addressing

o 11.5 Perfect hashing

o Problems

o Chapter notes

* 12 Binary Search Trees

o 12.1 What is a binary search tree?

o 12.2 Querying a binary search tree

o 12.3 Insertion and deletion

o 12.4 Randomly built binary search trees

o Problems

o Chapter notes

* 13 Red-Black Trees

o 13.1 Properties of red-black trees

o 13.2 Rotations

o 13.3 Insertion

o 13.4 Deletion

o Problems

o Chapter notes

* 14 Augmenting Data Structures

o 14.1 Dynamic order statistics

o 14.2 How to augment a data structure

o 14.3 Interval trees

o Problems

o Chapter notes

 

IV Advanced Design and Analysis Techniques

* 15 Dynamic Programming

o 15.1 Rod cutting

o 15.2 Matrix-chain multiplication

o 15.3 Elements of dynamic programming

o 15.4 Longest common subsequence

o 15.5 Optimal binary search trees

o Problems

o Chapter notes

* 16 Greedy Algorithms

o 16.1 An activity-selection problem

o 16.2 Elements of the greedy strategy

o 16.3 Huffman codes

o 16.4 Matroids and greedy methods

o 16.5 A task-scheduling problem as a matroid

o Problems

o Chapter notes

* 17 Amortized Analysis

o 17.1 Aggregate analysis

o 17.2 The accounting method

o 17.3 The potential method

o 17.4 Dynamic tables

o Problems

o Chapter notes

 

V Advanced Data Structures

* 18 B-Trees

o 18.1 De.nition of B-trees

o 18.2 Basic operations on B-trees

o 18.3 Deleting a key from a B-tree

o Problems

o Chapter notes

* 19 Fibonacci Heaps

o 19.1 Structure of Fibonacci heaps

o 19.2 Mergeable-heap operations

o 19.3 Decreasing a key and deleting a node

o 19.4 Bounding the maximum degree

o Problems

o Chapter notes

* 20 van Emde Boas Trees

o 20.1 Preliminary approaches

o 20.2 A recursive structure

o 20.3 The van Emde Boas tree

o Problems

o Chapter notes

* 21 Data Structures for Disjoint Sets

o 21.1 Disjoint-set operations

o 21.2 Linked-list representation of disjoint sets

o 21.3 Disjoint-set forests

o 21.4 Analysis of union by rank with path compression

o Problems

o Chapter notes

 

VI Graph Algorithms

* 22 Elementary Graph Algorithms

o 22.1 Representations of graphs

o 22.2 Breadth-.rst search

o 22.3 Depth-.rst search

o 22.4 Topological sort

o 22.5 Strongly connected components

o Problems

o Chapter notes

* 23 Minimum Spanning Trees

o 23.1 Growing a minimum spanning tree

o 23.2 The algorithms of Kruskal and Prim

o Problems

o Chapter notes

* 24 Single-Source Shortest Paths

o 24.1 The Bellman-Ford algorithm

o 24.2 Single-source shortest paths in directed acyclic graphs

o 24.3 Dijkstra’s algorithm

o 24.4 Difference constraints and shortest paths

o 24.5 Proofs of shortest-paths properties

o Problems

o Chapter notes

* 25 All-Pairs Shortest Paths

o 25.1 Shortest paths and matrix multiplication

o 25.2 The Floyd-Warshall algorithm

o 25.3 Johnson’s algorithm for sparse graphs

o Problems

o Chapter notes

* 26 Maximum Flow

o 26.1 Flow networks

o 26.2 The Ford-Fulkerson method

o 26.3 Maximum bipartite matching

o 26.4 Push-relabel algorithms

o 26.5 The relabel-to-front algorithm

o Problems

o Chapter notes

 

VII Selected Topics

* 27 Multithreaded Algorithms

o 27.1 The basics of dynamic multithreading

o 27.2 Multithreaded matrix multiplication

o 27.3 Multithreaded merge sort

o Problems

o Chapter notes

* 28 Matrix Operations

o 28.1 Solving systems of linear equations

o 28.2 Inverting matrices

o 28.3 Symmetric positive-de.nite matrices and least-squares approximation

o Problems

o Chapter notes

* 29 Linear Programming

o 29.1 Standard and slack forms

o 29.2 Formulating problems as linear programs

o 29.3 The simplex algorithm

o 29.4 Duality

o 29.5 The initial basic feasible solution

o Problems

o Chapter notes

* 30 Polynomials and the FFT

o 30.1 Representing polynomials

o 30.2 The DFT and FFT

o 30.3 Ef.cient FFT implementations

o Problems

o Chapter notes

* 31 Number-Theoretic Algorithms

o 31.1 Elementary number-theoretic notions

o 31.2 Greatest common divisor

o 31.3 Modular arithmetic

o 31.4 Solving modular linear equations

o 31.5 The Chinese remainder theorem

o 31.6 Powers of an element

o 31.7 The RSA public-key cryptosystem

o 31.8 Primality testing

o 31.9 Integer factorization

o Problems

o Chapter notes

* 32 String Matching

o 32.1 The naive string-matching algorithm

o 32.2 The Rabin-Karp algorithm

o 32.3 String matching with .nite automata

o 32.4 The Knuth-Morris-Pratt algorithm

o Problems

o Chapter notes

* 33 Computational Geometry

o 33.1 Line-segment properties

o 33.2 Determining whether any pair of segments intersects

o 33.3 Finding the convex hull

o 33.4 Finding the closest pair of points

o Problems

o Chapter notes

* 34 NP-Completeness

o 34.1 Polynomial time

o 34.2 Polynomial-time veri.cation

o 34.3 NP-completeness and reducibility

o 34.4 NP-completeness proofs

o 34.5 NP-complete problems

o Problems

o Chapter notes

* 35 Approximation Algorithms

o 35.1 The vertex-cover problem

o 35.2 The traveling-salesman problem

o 35.3 The set-covering problem

o 35.4 Randomization and linear programming

o 35.5 The subset-sum problem

o Problems

o Chapter notes

 

VIII Appendix: Mathematical Background

* A Summations

o A.1 Summation formulas and properties

o A.2 Bounding summations

o Problems

o Appendix notes

* B Sets, Etc.

o B.1 Sets

o B.2 Relations

o B.3 Functions

o B.4 Graphs

o B.5 Trees

o Problems

o Appendix notes

* C Counting and Probability

o C.1 Counting

o C.2 Probability

o C.3 Discrete random variables

o C.4 The geometric and binomial distributions

o C.5 The tails of the binomial distribution

o Problems

o Appendix notes

* D Matrices

o D.1 Matrices and matrix operations

o D.2 Basic matrix properties

o Problems

o Appendix notes

Bibliography

Index

 

 

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