A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis

A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis


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A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis by Anne Benoit, Yves Robert, Frederic Vivien

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.

Product Details

ISBN-13: 9781439825648
Publisher: Taylor & Francis
Publication date: 08/30/2013
Series: Chapman & Hall/CRC Applied Algorithms and Data Structures Series , #6
Pages: 380
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

Strassen’s algorithm
Master theorem
Solving recurrences

Greedy Algorithms
Motivating example: the sports hall
Designing greedy algorithms
Graph coloring
Theory of matroids

Dynamic Programming
The coin changing problem
The knapsack problem
Designing dynamic-programming algorithms

Amortized Analysis
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
Problem classes
NP-complete problems and reduction theory
Examples of NP-complete problems and reductions
Importance of problem definition
Strong NP-completeness
Why does it matter?

Exercises on NP-Completeness
Easy reductions
About graph coloring
Scheduling problems
More involved reductions
2-PARTITION is NP-complete

Beyond NP-Completeness
Approximation results
Polynomial problem instances
Linear programming
Randomized algorithms
Branch-and-bound and backtracking

Exercises Going beyond NP-Completeness
Approximation results
Dealing with NP-complete problems

Reasoning on Problem Complexity
Reasoning to Assess a Problem Complexity

Basic reasoning
Set of problems with polynomial-time algorithms
Set of NP-complete problems

Chains-on-Chains Partitioning
Optimal algorithms for homogeneous resources
Variants of the problem
Extension to a clique of heterogeneous resources

Replica Placement in Tree Networks
Access policies
Complexity results
Variants of the replica placement problem

Packet Routing
MEDP: Maximum edge-disjoint paths
PRVP: Packet routing with variable-paths

Matrix Product, or Tiling the Unit Square
Problem motivation
A guaranteed heuristic
Related problems

Online Scheduling
Flow time optimization
Competitive analysis
Makespan optimization



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