Local graph partitions for approximation and testing

Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, Krzysztof Onak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

95 Scopus citations


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: • 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. • We show a simple proof that any minor-closed graph property is testable in constant time in the bounded degree model. • 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.

Original languageEnglish
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Number of pages10
StatePublished - 2009
Externally publishedYes
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: 25 Oct 200927 Oct 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Country/TerritoryUnited States
CityAtlanta, GA


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