Foundations of Algorithms

Name: Foundations of Algorithms
Price: 6.75 USD
Availability: InStock
ISBN: 9780763782504

ISBN-10: 0763782505

ISBN-13: 9780763782504

Edition: 4th 2011 (Revised)

Authors: Richard Neapolitan, Kumarss Naimipour

List price: $214.95

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Foundations of Algorithms, Fourth Edition offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity. The volume is accessible to mainstream computer science students who have a background in college algebra and discrete structures. To support their approach, the authors present mathematical concepts using standard English and a simpler notation than is found in most texts. A review of essential mathematical concepts is presented in three appendices. The authors also reinforce the explanations with numerous concrete examples to help students grasp theoretical concepts. A CD-ROM is included with every new copy of the text and…

Book details

List price: $214.95
Edition: 4th
Copyright year: 2011
Publisher: Jones & Bartlett Learning, LLC
Publication date: 12/28/2009
Binding: Hardcover
Pages: 627
Size: 7.25" wide x 9.00" long x 1.25" tall
Weight: 2.706

Richard E. Neapolitan is professor and Chair of Computer Science at Northeastern Illinois University. He has previously written four books including the seminal 1990 Bayesian network text Probabilistic Reasoning in Expert Systems. More recently, he wrote the 2004 text Learning Bayesian Networks, the textbook Foundations of Algorithms, which has been translated to three languages and is one of the most widely-used algorithms texts world-wide, and the 2007 text Probabilistic Methods for Financial and Marketing Informatics (Morgan Kaufmann Publishers).




Algorithms: Efficiency, Analysis, and Order



Algorithms



The Importance of Developing Efficient Algorithms



Sequential Search Versus Binary Search



The Fibonacci Sequence



Analysis of Algorithms



Complexity Analysis



Applying the Theory



Analysis of Correctness



Order



An Intuitive Introduction to Order



A Rigorous Introduction to Order



Using a Limit to Determine Order



Outline of This Book


Exercises



Divide-and-Conquer



Binary Search



Mergesort



The Divide-and-Conquer Approach



Quicksort (Partition Exchange Sort)



Strassen's Matrix Multiplication Algorithm



Arithmetic with Large Numbers



Representation of Large Integers: Addition and Other Linear-Time Operations



Multiplication of Large Integers



Determining Thresholds



When Not to Use Divide-and-Conquer


Exercises



Dynamic Programming



The Binomial Coefficient



Floyd's Algorithm for Shortest Paths



Dynamic Programming and Optimization Problems



Chained Matrix Multiplication



Optimal Binary Search Trees



The Traveling Salesperson Problem



Sequence Alignment


Exercises



The Greedy Approach



Minimum Spanning Trees



Prim's Algorithm



Kruskal's Algorithm



Comparing Prim's Algorithm with Kruskal's Algorithm



Final Discussion



Dijkstra's Algorithm for Single-Source Shortest Paths



Scheduling



Minimizing Total Time in the System



Scheduling with Deadlines



Huffman Code



Prefix Codes



Huffman's Algorithm



The Greedy Approach Versus Dynamic Programming: The Knapsack Problem



A Greedy Approach to the 0-1 Knapsack Problem



A Greedy Approach to the Fractional Knapsack Problem



A Dynamic Programming Approach to the 0-1 Knapsack Problem



A Refinement of the Dynamic Programming Algorithm for the 0-1 Knapsack Problem


Exercises



Backtracking



The Backtracking Technique



The n-Queens Problem



Using a Monte Carlo Algorithm to Estimate the Efficiency of a Backtracking Algorithm



The Sum-of-Subsets Problem



Graph Coloring



The Hamiltonian Circuits Problem



The 0-1 Knapsack Problem



A Backtracking Algorithm for the 0-1 Knapsack Problem



Comparing the Dynamic Programming Algorithm and the Backtracking Algorithm for the 0-1 Knapsack Problem


Exercises



Branch-and-Bound



Illustrating Branch-and-Bound with the 0-1 Knapsack Problem



Breadth-First Search with Branch-and-Bound Pruning



Best-First Search with Branch-and-Bound Pruning



The Traveling Salesperson Problem



Abductive Inference (Diagnosis)


Exercises



Introduction to Computational Complexity: The Sorting Problem



Computational Complexity



Insertion Sort and Selection Sort



Lower Bounds for Algorithms that Remove at Most One Inversion per Comparison



Mergesort Revisited



Quicksort Revisited



Heapsort



Heaps and Basic Heap Routines



An Implementation of Heapsort



Comparison of Mergesort, Quicksort, and Heapsort



Lower Bounds for Sorting Only by Comparison of Keys



Decision Trees for Sorting Algorithms



Lower Bounds for Worst-Case Behavior



Lower Bounds for Average-Case Behavior



Sorting by Distribution (Radix Sort)


Exercises



More Computational Complexity: The Searching Problem



Lower Bounds for Searching Only by Comparisons of Keys



Lower Bounds for Worst-Case Behavior



Lower Bounds for Average-Case Behavior



Interpolation Search



Searching in Trees



Binary Search Trees



B-Trees



Hashing



The Selection Problem: Introduction to Adversary Arguments



Finding the Largest Key



Finding Both the Smallest and Largest Keys



Finding the Second-Largest Key



Finding the kth-Smallest Key



A Probabilistic Algorithm for the Selection Problem


Exercises



Computational Complexity and intractability: An Introduction to the Theory of NP



Intractability



Input Size Revisited



The Three General Problems



Problems for Which Polynomial-Time Algorithms Have Been Found



Problems That Have Been Proven to Be Intractable



Problems That Have Not Been Proven to Be Intractable but for Which Polynomial-Time Algorithms Have Never Been Found



The Theory of NP



The Sets P and NP



NP-Complete Problems



NP-Hard, NP-Easy, and NP-Equivalent Problems



Handling NP-Hard Problems



An Approximation Algorithm for the Traveling Salesperson Problem



An Approximation Algorithm for the Bin-Packing Problem


Exercises



Number-Theoretic Algorithms



Number Theory Review



Composite and Prime Numbers



Greatest Common Divisor



Prime Factorization



Least Common Multiple



Computing the Greatest Common Divisor



Euclid's Algorithm



An Extension to Euclid's Algorithm



Modular Arithmetic Review



Group Theory



Congruency Modulo n



Subgroups



Solving Modular Linear Equations



Computing Modular Powers



Finding Large Prime Numbers



Searching for a Large Prime



Checking if a Number Is Prime



The RSA Public-Key Cryptosystem



Public-Key Cryptosystems



The RSA Cryptosystem


Exercises



Introduction to Parallel Algorithms



Parallel Architectures



Control Mechanism



Address-Space Organization



Interconnection Networks



The PRAM Model



Designing Algorithms for the CREW PRAM Model



Designing Algorithms for the CRCW PRAM Model


Exercises



Review of Necessary Mathematics



Notation



Functions



Mathematical Induction



Theorems and Lemmas



Logarithms



Definition and Properties of Logarithms



The Natural Logarithm



Sets



Permutations and Combinations



Probability



Randomness



The Expected Value


Exercises



Solving Recurrence Equations: With Applications to Analysis of Recursive Algorithms



Solving Recurrences Using Induction



Solving Recurrences Using the Characteristic Equation



Homogeneous Linear Recurrences



Nonhomogeneous Linear Recurrences



Change of Variables (Domain Transformations)



Solving Recurrences by Substitution



Extending Results for n, a Power of a Positive Constant b, to n in General



Proofs of Theorems


Exercises



Data Structures for Disjoint Sets


References


Index