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PODC

2011

ACM

2011

ACM

This work studies decision problems from the perspective of nondeterministic distributed algorithms. For a yes-instance there must exist a proof that can be veriﬁed with a distributed algorithm: all nodes must accept a valid proof, and at least one node must reject an invalid proof. We focus on locally checkable proofs that can be veriﬁed with a constant-time distributed algorithm. For example, it is easy to prove that a graph is bipartite: the locally checkable proof gives a 2-colouring of the graph, which only takes 1 bit per node. However, it is more diﬃcult to prove that a graph is not bipartite—it turns out that any locally checkable proof requires Ω(log n) bits per node. In this work we classify graph problems according to their local proof complexity, i.e., how many bits per node are needed in a locally checkable proof. We establish tight or near-tight results for classical graph properties such as the chromatic number. We show that the proof complexities form a natura...

Related Content

Added |
17 Sep 2011 |

Updated |
17 Sep 2011 |

Type |
Journal |

Year |
2011 |

Where |
PODC |

Authors |
Mika Göös, Jukka Suomela |

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