Vertex-Connectivity for Node Failure Identification in Boolean Network Tomography

Galesi, Nicola; Ranjbar, Fariba; Zito, Michele

doi:10.1007/978-3-030-34405-4_5

Cited by 3 publications

(4 citation statements)

References 24 publications

(29 reference statements)

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“…An interesting question, relevant to apply XPath with Agrid, is how to efficiently determine the minimum number of measurement paths sufficient to identify all the failures after Agrid is applied. Finally, new connections between maximal node identifiability and vertex connectivity were recently found in [12] which can be further explored in connection with embeddability.…”

Section: Discussionmentioning

confidence: 99%

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

Galesi

Ranjbar

2018

2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS)

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We study maximal identifiability, a measure recently introduced in Boolean Network Tomography to characterize networks' capability to localize failure nodes in end-to-end path measurements. We prove tight upper and lower bounds on the maximal identifiability of failure nodes for specific classes of network topologies, such as trees and d-dimensional grids, in both directed and undirected cases. We prove that directed d-dimensional grids with support n have maximal identifiability d using 2d(n − 1) + 2 monitors; and in the undirected case we show that 2d monitors suffice to get identifiability of d − 1. We then study identifiability under embeddings: we establish relations between maximal identifiability, embeddability and graph dimension when network topologies are modeled as DAGs. Our results suggest the design of networks over N nodes with maximal identifiability Ω(log N ) using O(log N ) monitors and a heuristic to boost maximal identifiability on a given network by simulating d-dimensional grids. We provide positive evidence of this heuristic through data extracted by exact computation of maximal identifiability on examples of small real networks. * A preliminary version of this paper appeared in [11].

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Section: Discussionmentioning

confidence: 99%

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

Galesi

Ranjbar

2018

2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS)

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“…The condition introduced as k-identifiability (for P) states that any two distinct node sets of size at most k can be separated by at least a path in P. k-identifiability initially introduced for link failure detection [10,14], was later studied with success also for node failure detection [2,6,8,[11][12][13]. If this condition is true for a set of measurements paths P it ensures that if there are at most k failure nodes in P then these nodes can be identified unambiguously.…”

Section: Previous Workmentioning

confidence: 99%

“…Our results culminated with a heuristic to design networks with a high degree of identifiability or to modify a network to boost identifiability. In the work [8] we were employing Menger's theorem establishing a precise relation of µ(P) with the vertex connectivity of the graph underlying P. We generalize results in [6] to Line-of-Sight Networks and started the study of identifiability conditions on random graphs and random regular graphs.…”

Section: Previous Workmentioning

confidence: 99%

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Counting and localizing defective nodes by Boolean network tomography

Galesi¹,

Ranjbar²

2021

Preprint

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Identifying defective items in larger sets is a main problem with many applications in real life situations. We consider the problem of localizing defective nodes in networks through an approach based on boolean network tomography (BNT), which is grounded on inferring informations from the boolean outcomes of end-to-end measurements paths. Identifiability conditions on the set of paths which guarantee discovering or counting unambiguously the defective nodes are of course very relevant. We investigate old and introduce new identifiability conditions contributing this problem both from a theoretical and applied perspective. ( 1) What is the precise tradeoff between number of nodes and number of paths such that at most k nodes can be identified unambiguously ? The answer is known only for k = 1 and we answer the question for any k, setting a problem implicitly left open in previous works. (2) We study upper and lower bounds on the number of unambiguously identifiable nodes, introducing new identifiability conditions which strictly imply and are strictly implied by unambiguous identifiability; (3) We use these new conditions on one side to design algorithmic heuristics to count defective nodes in a fine-grained way, on the other side to prove the first complexity hardness results on the problem of identifying defective nodes in networks via BNT. (4) We introduce a random model where we study lower bounds on the number of unambiguously identifiable defective nodes and we use this model to estimate that number on real networks by a maximum likelihood estimate approach.

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Tight bounds to localize failure nodes on trees, grids and through embeddings under boolean network tomography

Galesi

Ranjbar

2022

Theoretical Computer Science

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Vertex-Connectivity for Node Failure Identification in Boolean Network Tomography

Cited by 3 publications

References 24 publications

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

Counting and localizing defective nodes by Boolean network tomography

Tight bounds to localize failure nodes on trees, grids and through embeddings under boolean network tomography

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