Labeling Schemes for Vertex Connectivity

Korman, Amos

doi:10.1007/978-3-540-73420-8_11

Cited by 25 publications

(26 citation statements)

References 29 publications

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“…Finding tight bounds for the size of proof labeling schemes for such problems is challenging. In addition, it is natural to also try to find proof labeling schemes for various implicit labeling schemes such as the ones in [23,31,32].…”

Section: Resultsmentioning

confidence: 99%

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Proof labeling schemes

2010

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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 that the global property holds). In addition, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the bit complexity of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity, in the context of proof labeling schemes. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables the verification to be less costly sometimes, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify it, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.

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Section: Resultsmentioning

confidence: 99%

“…The (rather simple) upper bound proof is described in [32]. Informally, the idea behind the upper bound proof is the following.…”

Section: Lemma 33 the Proof Size Of F Distinct Overmentioning

confidence: 99%

Proof labeling schemes

2010

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“…(E.g., the distance labeling schemes in [15] and the flow and vertex connectivity labeling schemes in [17,20,23]. )…”

Section: Extending Labeling Schemesmentioning

confidence: 99%

Controller and estimator for dynamic networks

Korman¹,

Kutten²

2013

Information and Computation

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International audienceAfek, Awerbuch, Plotkin, and Saks identified an important fundamental problem inherent to distributed networks, which they called the Resource Controller problem. Consider, first, the problem in which one node (called the 'root') is required to estimate the number of events that occurred all over the network. This counting problem can be viewed as a useful variant of the heavily studied and used task of topology update (that deals with collecting all remote information). The Resource Controller problem generalizes the counting problem: such remote events are considered as requests, and the counting node, i.e., the 'root', also issues permits for the requests. That way, the number of requests granted can be controlled (bounded). An efficient Resource Controller was constructed in the paper by Afek et al., and it can operate on a dynamic network assuming that the network is spanned by a tree that may only grow, and only by allowing leaves to join the tree. In contrast, the Resource Controller presented here can operate under a more general dynamic model, allowing the spanning tree of the network to undergo both insertions and deletions of both leaves and internal nodes. Despite the more dynamic network model we allow, the message complexity of our controller is never more than the message complexity of the more restricted controller. All the applications for the controller of Afek et al. can be used also with our controller. Moreover, with the same message complexity, our controller can handle these applications under the more general dynamic model mentioned above. In particular, the new controller can be transformed into an efficient size-estimation protocol, i.e., a protocol allowing all nodes to maintain a constant factor estimation of the number of nodes in the dynamically changing network. Informally, the resulting new size-estimation protocol uses View the MathML source amortized message complexity per topological change (assuming that the number of changes in the network size is "not too small"), where n is the current number of nodes in the network. An application of the size estimation of Afek et al. was to solve agreement in the case of initial faults (Fischer, Lynch, and Paterson) and leader election under initial faults (Bar-Yehuda and Kutten). Hence, the controllers in this paper can be useful for these applications too

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“…Informative labeling schemes were also proposed for other decision problems, including distance [4,14,25], routing [12,26], flow [18,20], vertex connectivity [18,19], and nearest common ancestor [5,24].…”

Section: Related Workmentioning

confidence: 99%

An optimal ancestry scheme and small universal posets

Fraigniaud

Korman

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

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In this paper, we solve the ancestry problem, which was introduced more than twenty years ago by Kannan et al. [STOC '88], and is among the most well-studied problems in the field of informative labeling schemes. Specifically, we construct an ancestry labeling scheme for n-node trees with label size log 2 n + O(log log n) bits, thus matching the log 2 n + Ω(log log n) bits lower bound given by Alstrup et al. [SODA '03]. Besides its optimal label size, our scheme assigns the labels in linear time, and guarantees that any ancestry query can be answered in constant time.In addition to its potential impact in terms of improving the performances of XML search engines, our ancestry scheme is also useful in the context of partially ordered sets. Specifically, for any fixed integer k, our scheme enables the construction of a universal poset of size O(n k log 4k n) for the family of n-element posets with tree-dimension at most k. This bound is almost tight thanks to a lower bound of n k−o(1) due to Alon and Scheinerman [Order '88].

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Labeling Schemes for Vertex Connectivity

Cited by 25 publications

References 29 publications

Proof labeling schemes

Proof labeling schemes

Controller and estimator for dynamic networks

An optimal ancestry scheme and small universal posets

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