Cart (Loading....) | Create Account
Close category search window

Local Graph Partitions for Approximation and Testing

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)

We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class of bounded-degree graphs. These oracles utilize only local computation to consistently answer queries about a global partition that breaks the graph into small connected components by removing only a small fraction of the edges. We illustrate the power of this technique by using it to extend and simplify a number of previous approximation and testing results for sparse graphs, as well as to provide new results that were unachievable with existing techniques. For instance:1. We give constant-time approximation algorithms for the size of the minimum vertex cover, the minimum dominating set, and the maximum independent set for any class of graphs with an excluded minor.2. We show a simple proof that any minor-closed graph property is testable in constant time in the bounded degree model.3. We prove that it is possible to approximate the distance to almost any hereditary property in any bounded degree hereditary families of graphs. Hereditary properties of interest include bipartiteness, k-colorability, and perfectness.

Published in:

Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on

Date of Conference:

25-27 Oct. 2009

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.