Rumor Source Obfuscation on Irregular Trees

Fanti, Giulia; Oh, Sewoong; Ramchandran, Kannan; Viswanath, Pramod

doi:10.1145/2964791.2901471

Cited by 16 publications

(10 citation statements)

References 38 publications

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“…The motivation for studying randomly growing networks is twofold: on the one hand, in numerous applications networks grow over time and one wants to infer information about the entities of the network in general, and about the source of the network in particular. Examples include rumor spreading in social networks (see for example [33,34,35,60]), finding the source of a computer virus in a telecommunication network (see for example [59]) and the evolution of biological networks [54], to name a few. On the other hand, the rigorous study of randomly growing networks has also its own mathematical interest.…”

Section: Related Workmentioning

confidence: 99%

New results for the random nearest neighbor tree

Lyuben¹,

Mitsche²

2021

Preprint

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In this paper, for d ∈ N, we study the online nearest neighbor random tree in dimension d (d-NN tree for short) defined as follows. Fix the flat torus T d n of dimension d and area n, equipped with the metric inherited from the Euclidean metric of R d . Then, embed consecutively n vertices in T d n uniformly at random and let each vertex but the first one connect to its (already embedded) nearest neighbor. We show that a.a.s. the number of vertices of degree at least k ∈ N in the d-NN tree decreases exponentially with k, and we obtain en passant that the maximum degree of G n is of order Θ d (log n) a.a.s. Moreover, the number of copies of any finite tree in the d-NN tree is shown to be a.a.s. Θ d (n), and all aforementioned counts are, by a general concentration lemma that we show, tightly concentrated around their expectations. We also give explicit bounds for the number of leaves that are independent of the dimension. Next, we show that a.a.s. the height of a uniformly chosen vertex in)) log n independently of the dimension, and the diameter of T d n is a.a.s. (2e + o(1)) log n, again, independently of the dimension. Finally, we define a natural infinite version of a d-NN tree G ∞ via a Poisson Point Process in R d , where the vertices are equipped with uniform arrival times in [0, 1],and show that it corresponds to the local limit of the sequence of finite graphs (G n ) n≥1 . Moreover, we prove that a.s. G ∞ is locally finite, that the simple random walk on G ∞ is a.s. recurrent, and that a.s. G ∞ is connected.To the best of our knowledge, ours are the first rigorous results both in the finite and infinite setup of this model.

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Section: Related Workmentioning

confidence: 99%

New results for the random nearest neighbor tree

Lyuben¹,

Mitsche²

2021

Preprint

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“…This problem is of importance in deciding whether or not a computer network is under attack, for instance, or whether a product gets sold through word-of-mouth or thanks to the advertisement campaign (or both [29]). More specifically, the problem of source detection [32][33][34][35][36] or obfuscation [11][12][13] has been extensively studied. On the other side of the spectrum, both experimental and theoretical work has tackled the problem of modeling [7,17,37], predicting the growth [6,39], and controlling the spread of epidemics [9,10,14,18].…”

Section: :2 Jessica Hoffmann and Constantine Caramanismentioning

confidence: 99%

Learning Graphs from Noisy Epidemic Cascades

HoffmannJessica

Caramanis

2019

Proc. ACM Meas. Anal. Comput. Syst.

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We consider the problem of learning the weighted edges of a graph by observing the noisy times of infection for multiple epidemic cascades on this graph. Past work has considered this problem when the cascade information, i.e., infection times, are known exactly. Though the noisy setting is well motivated by many epidemic processes (e.g., most human epidemics), to the best of our knowledge, very little is known about when it is solvable. Previous work on the no-noise setting critically uses the ordering information. If noise can reverse this-a node's reported (noisy) infection time comes after the reported infection time of some node it infected-then we are unable to see how previous results can be extended. We therefore tackle two versions of the noisy setting: the limited-noise setting, where we know noisy times of infections, and the extreme-noise setting, in which we only know whether or not a node was infected. We provide a polynomial time algorithm for recovering the structure of bidirectional trees in the extreme-noise setting, and show our algorithm matches lower bounds established in the no-noise setting, and hence is optimal. We extend our results for general degree-bounded graphs, where again we show that our (poly-time) algorithm can recover the structure of the graph with optimal sample complexity. We also provide the first efficient algorithm to learn the weights of the bidirectional tree in the limited-noise setting. Finally, we give a polynomial time algorithm for learning the weights of general bounded-degree graphs in the limited-noise setting. This algorithm extends to general graphs (at the price of exponential running time), proving the problem is solvable in the general case. All our algorithms work for any noise distribution, without any restriction on the variance. CCS Concepts: • Mathematics of computing → Graph theory; Graph algorithms; Probability and statistics; Computing most probable explanation; Combinatorics; • Networks → Network algorithms; • Theory of computation → Graph algorithms analysis; Sample complexity and generalization bounds; Random walks and Markov chains; Social networks.

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“…The focus in those works has been to understand the limit of information required in order to detect the epidemic. More generally, inverse problems have also been of interest, especially source detection [27,24,25,28,23] or obfuscation [12,11].…”

Section: Related Work and Backgroundmentioning

confidence: 99%

The Cost of Uncertainty in Curing Epidemics

HoffmannJessica

Caramanis

2018

SIGMETRICS Perform. Eval. Rev.

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Motivated by the study of controlling (curing) epidemics, we consider the spread of an SI process on a known graph, where we have a limited budget to use to transition infected nodes back to the susceptible state (i.e., to cure nodes). Recent work has demonstrated that under perfect and instantaneous information (which nodes are/are not infected), the budget required for curing a graph precisely depends on a combinatorial property called the CutWidth. We show that this assumption is in fact necessary: even a minor degradation of perfect information, e.g., a diagnostic test that is 99% accurate, drastically alters the landscape. Infections that could previously be cured in sublinear time now may require exponential time, or orderwise larger budget to cure. The crux of the issue comes down to a tension not present in the full information case: if a node is suspected (but not certain) to be infected, do we risk wasting our budget to try to cure an uninfected node, or increase our certainty by longer observation, at the risk that the infection spreads further? Our results present fundamental, algorithm-independent bounds that tradeoff budget required vs. uncertainty.

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Rumor Source Obfuscation on Irregular Trees

Cited by 16 publications

References 38 publications

New results for the random nearest neighbor tree

New results for the random nearest neighbor tree

Learning Graphs from Noisy Epidemic Cascades

The Cost of Uncertainty in Curing Epidemics

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