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FOCS

2009

IEEE

2009

IEEE

—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...

Related Content

Added |
20 May 2010 |

Updated |
20 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
FOCS |

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

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