Jessica Hoffmann
Abstract
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.
- Ery Arias-castro, Emmanuel J Candès, and Arnaud Durand. 2011. Detection of an anomalous cluster in a network. 39, 1 (2011), 278--304. arXiv:arXiv:1001.3209v2Google Scholar
- Ery Arias-Castro, Emmanuel J. Candès, Hannes Helgason, and Ofer Zeitouni. 2008. Searching for a trail of evidence in a maze. Annals of Statistics 36, 4 (2008), 1726--1757. arXiv:math/0701668Google ScholarCross Ref
- Ery Arias-castro and S T Nov. {n. d.}. Detecting a Path of Correlations in a Network. ({n. d.}), 1--12. arXiv:arXiv:1511.01009v1Google Scholar
- Daniel Bernoulli and Sally Blower. 2004. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Reviews in medical virology 14 (2004), 275--288.Google Scholar
- Abhijit Bose, Xin Hu, Kang G. Shin, and Taejoon Park. 2008. Behavioral Detection of Malware on Mobile Handsets. In Proceedings of the 6th International Conference on Mobile Systems, Applications, and Services (MobiSys '08). ACM, New York, NY, USA, 225--238. Google ScholarDigital Library
- Daniel G Brown. {n. d.}. How I wasted too long finding a concentration inequality for sums of geometric variables. Found at https://cs. uwaterloo. ca/? browndg/negbin. pdf 6 ({n. d.}).Google Scholar
- Thomas M Cover and Joy A Thomas. 2012. Elements of information theory. John Wiley & Sons.Google Scholar
- Kimon Drakopoulos, Asuman Ozdaglar, and John N. Tsitsiklis. 2014. An efficient curing policy for epidemics on graphs. arXiv preprint arXiv:1407.2241 December (2014), 1--10. arXiv:arXiv:1407.2241v1Google Scholar
- Kimon Drakopoulos, Asuman Ozdaglar, and John N. Tsitsiklis. 2015. A lower bound on the performance of dynamic curing policies for epidemics on graphs. 978 (2015), 3560--3567. arXiv:1510.06055Google Scholar
- Kimon Drakopoulos, Asuman Ozdaglar, and John N. Tsitsiklis. 2015. When is a network epidemic hard to eliminate? (2015), 1--17. arXiv:1510.06054 http://arxiv.org/abs/1510.06054Google Scholar
- Giulia Fanti, Peter Kairouz, Sewoong Oh, Kannan Ramchandran, and Pramod Viswanath. 2016. Rumor source obfuscation on irregular trees. In Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science. ACM, 153--164. Google ScholarDigital Library
- Giulia Fanti, Peter Kairouz, Sewoong Oh, and Pramod Viswanath. 2015. Spy vs. spy: Rumor source obfuscation. In ACM SIGMETRICS Performance Evaluation Review, Vol. 43. ACM, 271--284. Google ScholarDigital Library
- Robert Gallager. 2013. Stochastic Processes: 9 - Random Walks, Large Deviations, and Martingales. Stochastic Processes (2013).Google Scholar
- Ayalvadi Ganesh, Laurent Massoulié, and Don Towsley. 2005. The effect of network topology on the spread of epidemics. In INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE, Vol. 2. IEEE, 1455--1466.Google ScholarCross Ref
- David Grimmett, Geoffrey Stirzaker. 2001. Probability and random processes. Oxford university press.Google Scholar
- Grégoire Jacob, Hervé Debar, and Eric Filiol. 2008. Behavioral detection of malware: from a survey towards an established taxonomy. Journal in Computer Virology 4, 3 (2008), 251--266.Google ScholarCross Ref
- Yishay Mansour. 2011. Lecture 5 : Lower Bounds using Information Theory Tools Distance between Distributions KL-Divergence. (2011).Google Scholar
- Eli A Meirom, Chris Milling, Constantine Caramanis, Shie Mannor, Sanjay Shakkottai, and Ariel Orda. 2015. Localized epidemic detection in networks with overwhelming noise. In ACM SIGMETRICS Performance Evaluation Review, Vol. 43. ACM, 441--442. Google ScholarDigital Library
- Chris Milling, Constantine Caramanis, Shie Mannor, and Sanjay Shakkottai. 2015. Distinguishing Infections on Different Graph Topologies. IEEE Transactions on Information Theory 61, 6 (2015), 3100--3120. arXiv:1309.6545Google ScholarCross Ref
- Chris Milling, Constantine Caramanis, Shie Mannor, and Sanjay Shakkottai. 2015. Local detection of infections in heterogeneous networks. Proceedings - IEEE INFOCOM 26 (2015), 1517--1525.Google Scholar
- Mark E. J. Newman. 2002. Spread of epidemic disease on networks. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 66, 1 (2002). arXiv:cond-mat/0205009Google ScholarCross Ref
- Ivan N. Sanov. 1961. On the Probability of Large Deviations of Random Variables. (1961), 213--224 pages.Google Scholar
- Devavrat Shah and Tauhid Zaman. 2010. Detecting sources of computer viruses in networks: theory and experiment. In ACM SIGMETRICS Performance Evaluation Review, Vol. 38. ACM, 203--214. Google ScholarDigital Library
- Devavrat Shah and Tauhid Zaman. 2011. Rumors in a network: Who's the culprit? IEEE Transactions on information theory 57, 8 (2011), 5163--5181. Google ScholarDigital Library
- Devavrat Shah and Tauhid Zaman. 2012. Rumor centrality: a universal source detector. In ACM SIGMETRICS Performance Evaluation Review, Vol. 40. ACM, 199--210. Google ScholarDigital Library
- James Sharpnack, Alessandro Rinaldo, and Aarti Singh. 2012. Changepoint detection over graphs with the spectral scan statistic. arXiv preprint 31 (2012), 1--14. arXiv:arXiv:1206.0773v1 http://arxiv.org/abs/1206.0773Google Scholar
- Sam Spencer and R Srikant. 2015. On the impossibility of localizing multiple rumor sources in a line graph. ACM SIGMETRICS Performance Evaluation Review 43, 2 (2015), 66--68. Google ScholarDigital Library
- Zhaoxu Wang, Wenxiang Dong, Wenyi Zhang, and Chee Wei Tan. 2014. Rumor source detection with multiple observations: Fundamental limits and algorithms. In ACM SIGMETRICS Performance Evaluation Review, Vol. 42. ACM, 1--13. Google ScholarDigital Library
Index Terms
- The Cost of Uncertainty in Curing Epidemics
Recommendations
The Cost of Uncertainty in Curing Epidemics
SIGMETRICS '18: Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer SystemsEpidemic models are used across biological and social sciences, engineering, and computer science, and have had important impact in the study of the dynamics of human disease and computer viruses, but also trends rumors, viral videos, and most recently ...
The Cost of Uncertainty in Curing Epidemics
SIGMETRICS '18Epidemic models are used across biological and social sciences, engineering, and computer science, and have had important impact in the study of the dynamics of human disease and computer viruses, but also trends rumors, viral videos, and most recently ...
Two-Step curing method for demoulding in UV nanoimprint lithography
In the UV nanoimprint lithography (UV NIL), it is obvious that the resist curing process is dependent on the UV dose, therefore three states of the resist pattern, i.e., uncuring, undercuring and full-curing may occur due to an inadequate curing control ...
Comments