Distributed verification of minimum spanning trees

Korman, Amos; Kutten, Shay

doi:10.1007/s00446-007-0025-1

Cited by 75 publications

(109 citation statements)

References 41 publications

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“…We define the class LCP( f ) that consists of graph properties that admit locally checkable proofs of size f (n) bits per node. This model is related to those studied by Korman et al [15,16,18,19] and Fraigniaud et al [11], but strictly stronger than both; see Section 3.…”

Section: Contributionssupporting

confidence: 81%

“…• proof labeling schemes of Korman et al [15,16,18,19], and • nondeterministic local decision of Fraigniaud et al [11].…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

“…The proof labeling scheme model of Korman et al [15,16,18,19] is inspired by the classical notion of labeling schemes (see Gavoille and Peleg [12] for a survey). In this model, (i) the verifier has run-time of 1 communication round, and (ii) a node cannot see the identifiers nor the input labels of its neighboring nodes.…”

Section: Proof Labeling Schemesmentioning

confidence: 99%

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Göös¹,

Suomela²

2016

Theory of Comput.

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Section: Contributionssupporting

confidence: 81%

“…• proof labeling schemes of Korman et al [15,16,18,19], and • nondeterministic local decision of Fraigniaud et al [11].…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

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Göös¹,

Suomela²

2016

Theory of Comput.

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“…However, one of the nodes in the bad instance has to raise an alarm-if we attempt to do this based on local information only, we will occasionally make false alarms. Even though the task is inherently global, we can still use local algorithms if we resort to proof labeling schemes [6,12,13]. If we are given just an arbitrary spanning tree T , we cannot verify it locally.…”

Section: Alarm Ok Okmentioning

confidence: 99%

Exploiting locality in distributed SDN control

Schmid

Suomela

2013

Proceedings of the Second ACM SIGCOMM Workshop on Hot Topics in Software Defined Networking

172

131

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Large SDN networks will be partitioned in multiple controller domains; each controller is responsible for one domain, and the controllers of adjacent domains may need to communicate to enforce global policies. This paper studies the implications of the local network view of the controllers. In particular, we establish a connection to the field of local algorithms and distributed computing, and discuss lessons for the design of a distributed control plane. We show that existing local algorithms can be used to develop efficient coordination protocols in which each controller only needs to respond to events that take place in its local neighborhood. However, while existing algorithms can be used, SDN networks also suggest a new approach to the study of locality in distributed computing. We introduce the so-called supported locality model of distributed computing. The new model is more expressive than the classical models that are commonly used in the design and analysis of distributed algorithms, and it is a better match with the features of SDN networks.

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“…Labeling schemes were also proposed for other decision problems on graphs, including distance [4,16,17,22,26,27,28,31,35], routing [12,24,36], flow [21,25], vertex connectivity [21,23], nearest common ancestor [5,32], tree sibling [4,13] and various other tree functions, such center, separation level, and Steiner weight of a given subset of vertices [32]. See [15] for a survey on labeling schemes.…”

Section: Introductionmentioning

confidence: 99%

Compact Ancestry Labeling Schemes for XML Trees

Fraigniaud¹,

Korman²

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

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An ancestry labeling scheme labels the nodes of any tree in such a way that ancestry queries between any two nodes can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of an ancestry scheme is by its label size, that is the maximum number of bits stored in a label, taken over all n-node trees. The design of ancestry labeling schemes finds applications in XML search engines. In these contexts, even small improvements in the label size are important. As a result, following the proposal of a simple interval based ancestry scheme with label size 2 log n bits (Kannan et al., STOC 88), a considerable amount of work was devoted to improve the bound on the label size. The current state of the art upper bound is log n + O( √ log n) bits (Abiteboul et al., SICOMP 06) which is still far from the known log n + Ω(log log n) lower bound (Alstrup et al., SODA 03). Motivated by the fact that typical XML trees have extremely small depth, this paper parameterizes the quality measure of an ancestry scheme not only by the number of nodes in the given tree but also by its depth. Our main result is the construction of an ancestry scheme that labels n-node trees of depth d with labels of size log n + 2 log d + O(1). In addition to our main result, we prove a result that may be of independent interest concerning the existence of a small universal graph for the family of trees with bounded depth.

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Distributed verification of minimum spanning trees

Cited by 75 publications

References 41 publications

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Exploiting locality in distributed SDN control

Compact Ancestry Labeling Schemes for XML Trees

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