2010
DOI: 10.1007/s00446-010-0095-3
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Abstract: This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as "how expensive is local verification?" and more specifically, "how expensive is local verification compared to computation?" A suitable model is introduced in which these questions are studied in terms of the number of bits a vertex needs to communicate. The model includes the definition of a proof labeling scheme (a pair of algorithmsone to assign the labels, and one to use them to verify th… Show more

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Cited by 173 publications
(234 citation statements)
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“…Following the paradigm of algorithms with advice [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,44,49], this information is provided to the agents at the start of their navigation by an oracle that knows the network, the starting positions of the agents and, in the case of treasure hunt, the node where the treasure is hidden. The oracle assists the agents by providing them with a binary string called advice, which can be used by the agent during the algorithm execution.…”
Section: Model and Problemsmentioning
confidence: 99%
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“…Following the paradigm of algorithms with advice [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,44,49], this information is provided to the agents at the start of their navigation by an oracle that knows the network, the starting positions of the agents and, in the case of treasure hunt, the node where the treasure is hidden. The oracle assists the agents by providing them with a binary string called advice, which can be used by the agent during the algorithm execution.…”
Section: Model and Problemsmentioning
confidence: 99%
“…Providing nodes or agents with information of arbitrary type that can be used to perform network tasks more efficiently has been proposed in [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,42,44,49]. This approach was referred to as algorithms with advice.…”
Section: Related Workmentioning
confidence: 99%
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“…In [22], given a distributed representation of a solution for a problem, the authors investigated the number of bits of communication needed to verify the legality of the represented solution. In [13] the authors compared the minimum size of advice required to solve two information dissemination problems using a linear number of messages.…”
Section: Introductionmentioning
confidence: 99%
“…As for distributed decision, each node just outputs a boolean, and the global decision is the logical conjunction of these booleans. Moreover, [9,19] proved that Ω(log n)-bit certificates are necessary for verifying trees. In [3], the size of the certificates is nevertheless decreased to constant, by allowing nodes to output just 2 bits instead of 1.…”
mentioning
confidence: 99%