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Introduction to the Design and Analysis of Algorithms
Anany Levitin, Villanova University

ISBN-10: 0201743957
ISBN-13:  9780201743951

Publisher:  Addison-Wesley
Copyright:  2003
Format:  Cloth; 528 pp
Published:  10/30/2002
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Description

Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a truly innovative manner. Written in a student-friendly style, the book encourages broad problem-solving skills while thoroughly covering the material required in an introductory algorithms course. The author emphasizes conceptual understanding before the introduction of the formal treatment of each technique. Popular puzzles are used to motivate students' interest and strengthen their skills in algorithmic problem solving. Other learning-enhancement features include chapter summaries, hints to the exercises, and a solution manual.


Features

  • Covers both design and analysis frameworks.
  • Employs an innovative and more comprehensive taxonomy of algorithm design techniques.
  • Covers mathematical analysis of both nonrecursive and recursive algorithms, as well as empirical analysis and algorithm visualization.
  • Discusses limitations of algorithms and ways to overcome them.
  • Treats algorithms as problem-solving tools and develops algorithmic thinking by using puzzles and games.
  • Contains over 600 exercises with hints for students and solutions for instructors.
  • Includes material suggested by ACM Curriculum 2001.


Table of Contents

(Each chapter ends with a “Summary”.)

Preface.


1. Introduction.

The notion of algorithm.

Fundamentals of algorithmic problem solving.

Important problem types.

Fundamental data structures.



2. Fundamentals of the Analysis of Algorithm Efficiency.

Analysis framework.

Asymptotic notations and standard efficiency classes.

Mathematical analysis of nonrecursive algorithms.

Mathematical analysis of recursive algorithms.

Example: Fibonacci numbers.

Empirical analysis of algorithms.

Algorithm visualization.



3. Brute Force.

Selection sort and bubble sort.

Sequential search and brute-force string matching.

The closest-pair and convex-hull problems by brute force.

Exhaustive search.



4. Divide-and-Conquer.

Mergesort.

Quicksort.

Binary search.

Binary tree traversals and related properties.

Multiplication of large integers and Strassen's matrix multiplication.

Closest-pair and convex-hull problems by divide-and-conquer.



5. Decrease-and-Conquer.

Insertion sort.

Depth-first search and breadth-first search.

Topological sorting.

Algorithms for generating combinatorial objects.

Decrease-by-a-constant-factor algorithms.

Variable-size-decrease algorithms.



6. Transform-and-conquer.

Presorting.

Gaussian elimination.

Balanced search trees.

Heaps and heapsort.

Horner's rule and binary exponentiation.

Problem reduction.



7. Space and Time Tradeoffs.

Sorting by counting.

Horspool's and Boyer-Moore algorithms for string matching.

Hashing.

B-trees.



8. Dynamic Programming.

Computing a binomial coefficient.

Shortest-path problems.

Warshall's and Floyd's algorithms.

Optimal binary search trees.

The knapsack problem and memory functions.



9. Greedy Technique.

Prim's algorithm.

Kruskal's algorithm.

Dijkstra's algorithm.

Huffman trees.



10. Limitations of Algorithm Power.

Lower-bound arguments.

Decision trees.

P, NP, and NP-complete problems.

Challenges of numerical algorithms.



11. Coping with the Limitations of Algorithm Power.

Backtracking.

Branch-and-bound.

Approximation algorithms for NP-hard problems.

Algorithms for solving nonlinear equations.



Epilogue.


Appendix A: Useful Formulas for the Analysis of Algorithms.


Appendix B: Short Tutorial on Recurrence Relations.


Bibliography.


Hints to Exercises.


Index.



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