Signaling Free Localization of Node Failures in All-Optical Networks

Tapolcai, János; Rónyai, Lajos; Hosszú, Éva; Gyimothi, Laszlo; Ho, Pin–Han; Subramaniam, Suresh

doi:10.1109/tcomm.2016.2545653

Cited by 5 publications

(16 citation statements)

References 28 publications

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“…Inspired by the node failure localization model of Tapolcai et al [27,28] we introduce a possible new feature of the elements. Informally speaking an element can be kind of smart and this fact means two things:…”

Section: New Feature Of the Elementsmentioning

confidence: 99%

“…A version of the previously mentioned problem already appeared in the literature. In [27,28] failures in a network are checked by monitoring trails that turn into off state if interrupted by a failure event. The goal is to construct the monitoring trails such a way that any node can determine the network failure status solely by observing the on-off status of the monitoring trails traversing that node.…”

Section: Possible Applications Of Smart Elementsmentioning

confidence: 99%

“…However, the lower bound proved in [27,28] does not use this property, but deals with the abstract setting studied in this paper. We improve their lower bound in Corollary 16.…”

Section: Possible Applications Of Smart Elementsmentioning

confidence: 99%

“…

In combinatorial group testing problems the questioner needs to find a special element x ∈ [n] by testing subsets of [n]. Tapolcai et al [27,28] introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one.Using classical results of extremal set theory we prove that if F n ⊆ 2 [n] solves the nonadaptive version of this problem and has minimal cardinality, then lim n→∞ |F n | log 2 n = log (3/2) 2.This improves results in [27,28].We also consider related models inspired by secret sharing models, where the elements should share information among them to find out the special one. Finally the adaptive versions of the different models are investigated.and for F ⊆ [n] the answer is the appropriate value of the function t :The tested subsets are called queries and the special element is usually called defective in the group testing literature.

…”

mentioning

confidence: 99%

“…In combinatorial group testing problems the questioner needs to find a special element x ∈ [n] by testing subsets of [n]. Tapolcai et al [27,28] introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one.…”

mentioning

confidence: 99%

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Smart elements in combinatorial group testing problems

Gerbner

Vizer

2018

J Comb Optim

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In combinatorial group testing problems the questioner needs to find a special element x ∈ [n] by testing subsets of [n]. Tapolcai et al. [27,28] introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one.Using classical results of extremal set theory we prove that if F n ⊆ 2 [n] solves the nonadaptive version of this problem and has minimal cardinality, then lim n→∞ |F n | log 2 n = log (3/2) 2.This improves results in [27,28].We also consider related models inspired by secret sharing models, where the elements should share information among them to find out the special one. Finally the adaptive versions of the different models are investigated.and for F ⊆ [n] the answer is the appropriate value of the function t :The tested subsets are called queries and the special element is usually called defective in the group testing literature. Questioner's aim is to ask as few queries as possible and the number of queries needed to ask in the worst case is called the worst-case complexity of the problem. For any combinatorial group testing problem there are at least two main approaches: whether it is adaptive or non-adaptive. In the adaptive scenario Questioner asks queries depending on the answers for the previously asked queries, however in the non-adaptive version Questioner must pose all the queries at the beginning.Let us briefly describe the solution for the (above mentioned) most basic combinatorial group testing model in the non-adaptive case. We call a family F ⊆ 2 [n] separating if for any two different x, y ∈ [n] there is F ∈ F with x ∈ F and y ∈ F, or y ∈ F and x ∈ F.Fact 1. Questioner finds the defective by asking elements of F ⊆ 2 [n] if and only if F is separating.The notion of separating family in the context of combinatorial group testing was introduced and first studied by Rényi in [23]. We will also use the following simple fact later:Fact 2. Suppose F n ⊆ 2 [n] is the smallest separating family. Then we have:|F n | = ⌈log 2 n⌉.One can imagine many possible generalizations of the most basic classical model: more defectives, other answers (threshold [6] or density [13] group testing), average case complexity [4], rounds [7, 15]. For a survey on different non-adaptive models see e.g. [10]. Combinatorial group testing problems were first considered during the World War II by Dorfman [9] in the context of mass blood testing. Since then group testing techniques have had many different applications, for example in fault diagnosis in optical networks [17], in quality control in product testing [25] or failure detection in wireless sensor networks [21]. New feature of the elementsInspired by the node failure localization model of Tapolcai et al. [27,28] we introduce a possible new feature of the elements. Informally speaking an element can be kind of smart and this fact means two things:

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Section: New Feature Of the Elementsmentioning

confidence: 99%

Section: Possible Applications Of Smart Elementsmentioning

confidence: 99%

“…However, the lower bound proved in [27,28] does not use this property, but deals with the abstract setting studied in this paper. We improve their lower bound in Corollary 16.…”

Section: Possible Applications Of Smart Elementsmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Smart elements in combinatorial group testing problems

Gerbner

Vizer

2018

J Comb Optim

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Greedy computation of all-optical monitoring trails to minimize total monitoring cost

Ogino

Kitahara

2019

Optical Switching and Networking

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Performance Limitation of Group Testing in Network Failure Detection

Xu,

Azuma,

Ariizumi

et al. 2023

IEEE Access

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In a network system, there inevitably be a few connection failures at nodes, such as delay. Once a failure occurs, the network administrator must detect failure sources as soon as possible to maintain communication over the network. Group testing is a method for detecting failure nodes in networks using a small number of measurements, provided that the measurement matrix is constructed appropriately. A promising method for constructing measurement matrices is given by the binary correlation matrices. This study analyzes the performance limitation of group testing based on the binary correlation measurement matrix. We derive the upper and lower bounds of the minimum number of measurements needed for network detection. Moreover, we propose a sufficient condition of network topology, under which the failure vertices in the network can be detected with optimal performance, and we also provide a detection scheme with guaranteed exactness for the network. Numerical example indicates that for the network that satisfies the proposed sufficient condition, the administrator can exactly detect the failure vertices with optimal performance by using our proposed detection scheme.

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Signaling Free Localization of Node Failures in All-Optical Networks

Cited by 5 publications

References 28 publications

Smart elements in combinatorial group testing problems

Smart elements in combinatorial group testing problems

Greedy computation of all-optical monitoring trails to minimize total monitoring cost

Performance Limitation of Group Testing in Network Failure Detection

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