Iterative Methods in Combinatorial Optimization

By: Lap Chi Lau, R. Ravi, Mohit Singh

Write A Review

Paperback | 18 April 2011

At a Glance

Paperback
256 Pages

Dimensions(cm)
22.9 x 15.7 x 1.4

Paperback

RRP $93.95

$84.75

10%OFF

or 4 interest-free payments of $21.19 with

Ships in 5 to 7 business days

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Mathematics Optimisation Computer Programming & Software Development Algorithms & Data Structures Combinatorics & Graph Theory

Preface	p. ix
Introduction	p. 1
The assignment problem	p. 1
Iterative algorithm	p. 3
Approach outline	p. 5
Context and applications of iterative rounding	p. 8
Book chapters overview	p. 8
Notes	p. 10
Preliminaries	p. 12
Linear programming	p. 12
Graphs and digraphs	p. 19
Submodular and supermodular functions	p. 21
Matching and vertex cover in bipartite graphs	p. 28
Matchings in bipartite graphs	p. 28
Generalized assignment problem	p. 32
Maximum budgeted allocation	p. 35
Vertex cover in bipartite graphs	p. 40
Vertex cover and matching: duality	p. 43
Notes	p. 44
Spanning trees	p. 46
Minimum spanning trees	p. 46
Iterative 1-edge-finding algorithm	p. 54
Minimum bounded-degree spanning trees	p. 57
An additive one approximation algorithm	p. 60
Notes	p. 62
Matroids	p. 65
Preliminaries	p. 65
Maximum weight basis	p. 67
Matroid intersection	p. 71
Duality and min-max theorem	p. 74
Minimum bounded degree matroid basis	p. 77
k matroid intersection	p. 82
Notes	p. 85
Arborescence and rooted connectivity	p. 88
Minimum cost arborescence	p. 89
Minimum cost rooted k-connected subgraphs	p. 95
Minimum bounded degree arborescence	p. 101
Additive performance guarantee	p. 106
Notes	p. 108
Submodular flows and applications	p. 110
The model and the main result	p. 110
Primal integrality	p. 112
Dual integrality	p. 116
Applications of submodular flows	p. 117
Minimum bounded degree submodular flows	p. 124
Notes	p. 128
Network matrices	p. 131
The model and main results	p. 131
Primal integrality	p. 133
Dual integrality	p. 136
Applications	p. 139
Notes	p. 143
Matchings	p. 145
Graph matching	p. 145
Hypergraph matching	p. 155
Notes	p. 160
Network design	p. 164
Survivable network design problem	p. 164
Connection to the traveling salesman problem	p. 168
Minimum bounded degree Steiner networks	p. 172
An additive approximation algorithm	p. 175
Notes	p. 179
Constrained optimization problems	p. 182
Vertex cover	p. 182
Partial vertex cover	p. 184
Multicriteria spanning trees	p. 187
Notes	p. 189
Cut problems	p. 191
Triangle cover	p. 191
Feedback vertex set on bipartite tournaments	p. 194
Node multiway cut	p. 197
Notes	p. 200
Iterative relaxation: Early and recent examples	p. 203
A discrepancy theorem	p. 203
Rearrangments of sums	p. 206
Minimum cost circulation	p. 208
Minimum cost unsplittable flow	p. 210
Bin packing	p. 212
Iterative randomized rounding: Steiner trees	p. 220
Notes	p. 228
Summary	p. 231
Bibliography	p. 233
Index	p. 241
Table of Contents provided by Ingram. All Rights Reserved.

Iterative Methods in Combinatorial Optimization

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Optimisation

The Infinite Game

From the bestselling author of Start With Why

The Selfish Gene

40th Anniversary Edition

The Art of Strategy

A Game Theorist's Guide to Success in Business and Life

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

Statistical Analysis with R For Dummies

For Dummies (Computer/Tech)

Elementary Linear Algebra

8th Edition - International Metric Edition

On the Edge

The Art of Risking Everything

This Is Chaos: Embracing the Future of Magic

15 Essays on Chaos Magic for Modern Practitioners

Blackjack Mathematics for Non-Mathematicians

Fuzzy Sets and Triangular Norms

Aggregation in Decision-Aided Intelligent Systems

Advanced Techniques in Tracking and Sensor Management

Theory and Applications

AK Peters/CRC Recreational Mathematics

60 Years of Mathematical Puzzles in Parabola

Beautiful Security

When Science Meets Cybersecurity

Blackjack Mathematics for Non-Mathematicians

AK Peters/CRC Recreational Mathematics Series

Classical and Modern Optimization Techniques Applied to Control and Modeling

Foundation Engineering Mathematics

Engineering Mathematics and Operations Research

Swarm Optimization for Biomedical Applications

A Course in Behavioral Economics

3rd edition

Optimization

A Bootcamp for Machine Learning, Inverse Problems, and Control

Generative AI and Optimization Techniques for Sustainable Water Management

Springer Optimization and Its Applications

New Frontiers in Homogenization and Fractional Calculus

Trends in Mathematics

PDEs, Control and Deep Learning

Cetraro, Italy 2024

Energy Storage for Renewable Energy Systems

Modeling, Control, and AI Integration

Optimization Techniques for Deep Learning

Improving Performance and Efficiency

This product is categorised by