Presenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems.
Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem.
- Part I helps readers understand the main design principles and design efficient algorithms.
- Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness.
- Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard.
Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond.
|Publisher:||Taylor & Francis|
|Series:||Chapman & Hall/CRC Applied Algorithms and Data Structures Series , #6|
|Product dimensions:||6.20(w) x 9.30(h) x 0.90(d)|
About the Author
Yves Robert, École Normale Supérieure de Lyon, Institut Universitaire de France, and Université de Lyon, France
Anne Benoit and Frederic Vivien, École Normale Supérieure de Lyon, France
Table of Contents
Polynomial-Time Algorithms: Exercises
Introduction to Complexity
On the complexity to compute xn
Asymptotic notations: O, o, Θ, and Ω
Motivating example: the sports hall
Designing greedy algorithms
Theory of matroids
The coin changing problem
The knapsack problem
Designing dynamic-programming algorithms
Methods for amortized analysis
Exercises, Solutions, and Bibliographic Notes appear at the end of each chapter in this section.
NP-Completeness and Beyond
A practical approach to complexity theory
NP-complete problems and reduction theory
Examples of NP-complete problems and reductions
Importance of problem definition
Why does it matter?
Exercises on NP-Completeness
About graph coloring
More involved reductions
2-PARTITION is NP-complete
Polynomial problem instances
Branch-and-bound and backtracking
Exercises Going beyond NP-Completeness
Dealing with NP-complete problems
Reasoning on Problem Complexity
Reasoning to Assess a Problem Complexity
Set of problems with polynomial-time algorithms
Set of NP-complete problems
Optimal algorithms for homogeneous resources
Variants of the problem
Extension to a clique of heterogeneous resources
Replica Placement in Tree Networks
Variants of the replica placement problem
MEDP: Maximum edge-disjoint paths
PRVP: Packet routing with variable-paths
Matrix Product, or Tiling the Unit Square
A guaranteed heuristic
Flow time optimization