On the Impossibility of Localizing Multiple Rumor Sources in a Line Graph

Spencer, Sam; Srikant, R.

doi:10.1145/2825236.2825262

Cited by 19 publications

(9 citation statements)

References 2 publications

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“…The study of epidemics on graphs is an active field of research. An important body of work assumes the underlying graph is known, and focuses on modeling epidemics [19,75,32,16,78,47], detecting whether there is an epidemic [8,9,54,53,51,44,40], finding communities [60,76], localizing the source of the spread [65,66,64,69,72,70,20] or instead obfuscating it [26,28,27], or controlling their spread [43,21,22,34,29,71,77,58]. The inverse problem, recovering the network from epidemic data, has also been extensively studied [56,1,18,59,41,35,33].…”

Section: Relevant Workmentioning

confidence: 99%

Quarantines as a Targeted Immunization Strategy

Hoffmann,

Jordan,

Caramanis

2020

Preprint

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In the context of the recent COVID-19 outbreak, quarantine has been used to "flatten the curve" and slow the spread of the disease.In this paper, we show that this is not the only benefit of quarantine for the mitigation of an SIR epidemic spreading on a graph. Indeed, we theoretically prove that nodes of high-degree are disproportionately in the Removed state after a first wave of infection, which has very positive consequences. In particular, powerlaw graphs do not retain their structure after a few waves of infection, which implies second and third waves may be of much smaller amplitude than the first wave. We propose an opening and closing strategy aiming at immunizing the graph while infecting the minimum number of individuals, while guaranteeing the population is now robust to future infections. We experimentally verify our results on simulated networks.

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Section: Relevant Workmentioning

confidence: 99%

Quarantines as a Targeted Immunization Strategy

Hoffmann,

Jordan,

Caramanis

2020

Preprint

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“…Further avenues to explore related to our work include game-theoretic formulations [9], optimal sensor/spy placement [15], confidence sets for the source [7], and multiple rumor sources [14].…”

Section: Discussionmentioning

confidence: 99%

Rumor source detection with multiple observations under adaptive diffusions

Rácz¹,

Richey²

2020

Preprint

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Recent work, motivated by anonymous messaging platforms, has introduced adaptive diffusion protocols which can obfuscate the source of a rumor: a "snapshot adversary" with access to the subgraph of "infected" nodes can do no better than randomly guessing the entity of the source node. What happens if the adversary has access to multiple independent snapshots? We study this question when the underlying graph is the infinite d-regular tree. We show that (1) a weak form of source obfuscation is still possible in the case of two independent snapshots, but (2) already with three observations there is a simple algorithm that finds the rumor source with constant probability, regardless of the adaptive diffusion protocol. We also characterize the tradeoff between local spreading and source obfuscation for adaptive diffusion protocols (under a single snapshot). These results raise questions about the robustness of anonymity guarantees when spreading information in social networks.

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“…It has been recently shown that it is difficult to locate multiple sources [35]. It might be possible to spread the messages faster than adaptive diffusion and still achieve perfect obfuscation by creating multiple pseudo-sources.…”

Section: Discussionmentioning

confidence: 99%

Rumor Source Obfuscation on Irregular Trees

Fanti

Ramchandran

et al. 2016

SIGMETRICS Perform. Eval. Rev.

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Anonymous messaging applications have recently gained popularity as a means for sharing opinions without fear of judgment or repercussion. Messages in these applications propagate anonymously (without authorship metadata) over a network that is typically defined by social connections or physical proximity. However, recent advances in rumor source detection show that the source of such an anonymous message can be inferred by statistical inference attacks. Adaptive diffusion was recently proposed as a solution that achieves optimal source obfuscation over regular trees. However, in real social networks, node degrees differ from node to node, and adaptive diffusion can be significantly sub-optimal. This gap increases as the degrees become more irregular. In order to quantify this gap, we model the underlying network as coming from standard branching processes with i.i.d. degree distributions. Building upon the analysis techniques from branching processes, we give an analytical characterization of the dependence between the probability of detection achieved by adaptive diffusion and the degree distribution. Further, this analysis provides a key insight: passing a rumor to a friend who has many friends makes the source more ambiguous. This leads to a new family of protocols that we call Preferential Attachment Adaptive Diffusion (PAAD). When messages are propagated according to PAAD, we give both the MAP estimator for finding the source and also an analysis of the probability of detection achieved by this adversary. The analytical results are not directly comparable, since the adversary's observed information has a different distribution under adaptive diffusion than under PAAD. Instead, we present results from numerical experiments that suggest that PAAD achieves a lower probability of detection, at the cost of increased communication for coordination.

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On the Impossibility of Localizing Multiple Rumor Sources in a Line Graph

Cited by 19 publications

References 2 publications

Quarantines as a Targeted Immunization Strategy

Quarantines as a Targeted Immunization Strategy

Rumor source detection with multiple observations under adaptive diffusions

Rumor Source Obfuscation on Irregular Trees

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