Abstract
Given a graph, like a social/computer network or the blogosphere, in which an infection (or meme or virus) has been spreading for some time, how to select the k best nodes for immunization/quarantining immediately? Most previous works for controlling propagation (say via immunization) have concentrated on developing strategies for vaccination preemptively before the start of the epidemic. While very useful to provide insights in to which baseline policies can best control an infection, they may not be ideal to make real-time decisions as the infection is progressing.
In this paper, we study how to immunize healthy nodes, in the presence of already infected nodes. Efficient algorithms for such a problem can help public-health experts make more informed choices, tailoring their decisions to the actual distribution of the epidemic on the ground. First we formulate the Data-Aware Vaccination problem, and prove it is NP-hard and also that it is hard to approximate. Secondly, we propose three effective polynomial-time heuristics DAVA, DAVA-prune and DAVA-fast, of varying degrees of efficiency and performance. Finally, we also demonstrate the scalability and effectiveness of our algorithms through extensive experiments on multiple real networks including large epidemiology datasets (containing millions of interactions). Our algorithms show substantial gains of up to ten times more healthy nodes at the end against many other intuitive and nontrivial competitors.
- Roy M. Anderson and Robert M. May. 1991. Infectious Diseases of Humans. Oxford University Press, Oxford.Google Scholar
- James Aspnes, Kevin Chang, and Aleksandr Yampolskiy. 2005. Inoculation strategies for victims of viruses and the sum-of-squares partition problem. In Proceedings of the SODA, 43--52. Google ScholarDigital Library
- Norman Bailey. 1975. The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London.Google Scholar
- Christopher L. Barrett, Harry B. Hunt III, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz, Richard Edwin Stearns, and Mayur Thakur. 2008. Errata for the paper “Predecessor existence problems for finite discrete dynamical systems” {TCS 386 (1-2) (2007) 3-37}. Theor. Comput. Sci. 395, 1, 132--133. Google ScholarDigital Library
- Sushil Bikhchandani, David Hirshleifer, and Ivo Welch. 1992. A theory of fads, fashion, custom, and cultural change in informational cascades. J. Pol. Economy 100, 5 (October 1992), 992--1026.Google ScholarCross Ref
- Linda Briesemeister, Patric Lincoln, and Philip Porras. 2003. Epidemic profiles and defense of scale-free networks. In Proceedings of the WORM 2003 (October 27 2003). 67--75. Google ScholarDigital Library
- Adam L. Buchsbaum, Haim Kaplan, Anne Rogers, and Jeffery R. Westbrook. 1998. A new, simpler linear-time dominators algorithm. ACM Trans. Program. Lang. Syst. 20, 6 (November 1998), 1265--1296. Google ScholarDigital Library
- Po-An Chen, Mary David, and David Kempe. 2010a. Better vaccination strategies for better people. In Proceedings of the 11th ACM Conference on Electronic Commerce (EC’10). ACM, New York, NY, USA, 179--188. Google ScholarDigital Library
- W. Chen, C. Wang, and Y. Wang. 2010b. Scalable influence maximization for prevalent viral marketing in large-scale social networks. In Proceedings of the KDD. 1029--1038. Google ScholarDigital Library
- Reuven Cohen, Shlomo Havlin, and Daniel ben Avraham. 2003. Efficient immunization strategies for computer networks and populations. Phys. Rev. Lett. 91, 24 (Dec. 2003), 1--4.Google ScholarCross Ref
- Ron Cytron, Jeanne Ferrante, Barry K. Rosen, Mark N. Wegman, and F. Kenneth Zadeck. 1989. An efficient method of computing static single assignment form. In Proceedings of the 16th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 25--35. Google ScholarDigital Library
- J. Dushoff, J. B. Plotkin, C. Viboud, L. Simonsen, M. Miller, M. Loeb, and D. J. Earn. 2007. Vaccinating to protect a vulnerable subpopulation. PLoS Med. 4, 5, 0921--0927.Google ScholarCross Ref
- Stephen Eubank, Hasan Guclu, V. S. Anil Kumar, Madhav V. Marathe, Aravind Srinivasan, Zoltan Toroczkai, and Nan Wang. 2004. Modelling disease outbreaks in realistic urban social networks. Nature 429, 6988 (May 2004), 180--184.Google ScholarCross Ref
- N. M. Ferguson, D. A. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley, and D. S. Burke. 2006. Strategies for mitigating an influenza pandemic. Nature 442, 7101, 448--452.Google Scholar
- L. C. Freeman. 1977. A set of measures of centrality based on betweenness. Sociometry, 35--41.Google Scholar
- Ayalvadi Ganesh, Laurent Massoulié, and Don Towsley. 2005. The effect of network topology on the spread of epidemics. In IEEE INFOCOM. IEEE Computer Society Press, Los Alamitos, CA, 1455--1466.Google Scholar
- Samuel Goldberg. 1986. Probability: An Introduction. Courier Dover Publications, NY, USA.Google Scholar
- Jacob Goldenberg, Barak Libai, and Eitan Muller. 2001. Talk of the network: A complex systems look at the underlying process of word-of-mouth. Market. Lett. 12, 3, 211--223.Google ScholarCross Ref
- Amit Goyal, Francesco Bonchi, and Laks VS Lakshmanan. 2010. Learning influence probabilities in social networks. In Proceedings of the 3rd ACM International Conference on Web Search and Data Mining. ACM, 241--250. Google ScholarDigital Library
- D. Gruhl, R. Guha, D. Liben-Nowell, and A. Tomkins. 2004. Information diffusion through blogspace. In WWW’04. Retrieved from www.www2004.org/proceedings/docs/1p491.pdf. Google ScholarDigital Library
- M. Elizabeth Halloran, Neil M. Ferguson, Stephen Eubank, Ira M. Longini, Derek A. T. Cummings, Bryan Lewis, Shufu Xu, Christophe Fraser, Anil Vullikanti, Timothy C. Germann, Diane Wagener, Richard Beckman, Kai Kadau, Chris Barrett, Catherine A. Macken, Donald S. Burke, and Philip Cooley. 2008. Strategies for mitigating an influenza pandemic. Proc. Natl. Acad. Sci. 105, 12, 4639--4644.Google ScholarCross Ref
- Yukio Hayashi, Masato Minoura, and Jun Matsukubo. 2003. Recoverable prevalence in growing scale-free networks and the effective immunization. arXiv:cond-mat/0305549 v2 (August 6, 2003).Google Scholar
- H. W. Hethcote. 2000. The mathematics of infectious diseases. SIAM Rev. 42, 4, 599--653. Google ScholarDigital Library
- Glen Jeh and Jennifer Widom. 2003. Scaling personalized web search. In Proceedings of the 12th International Conference on World Wide Web (WWW’03). ACM, New York, NY, USA, 271--279. DOI:http://dx.doi.org/10.1145/775152.775191 Google ScholarDigital Library
- David Kempe, Jon Kleinberg, and Éva Tardos. 2003. Maximizing the spread of influence through a social network. In Conference of the ACM Special Interest Group on Knowledge Discovery and Data Mining. ACM Press, New York, NY, 137--146. Google ScholarDigital Library
- J. O. Kephart and S. R. White. 1993. Measuring and modeling computer virus prevalence. IEEE Computer Society Symposium on Research in Security and Privacy. 2--15. Google ScholarDigital Library
- Masahiro Kimura, Kazumi Saito, and Hiroshi Motoda. 2008. Minimizing the spread of contamination by blocking links in a network. In Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI’08). AAAI Press, 1175--1180. Google ScholarDigital Library
- Jon M. Kleinberg. 1998. Authoritative sources in a hyperlinked environment. In ACM-SIAM Symposium on Discrete Algorithms. 604--632. Google ScholarDigital Library
- Chris J. Kuhlman, Gaurav Tuli, Samarth Swarup, Madhav V. Marathe, and S. S. Ravi. 2013. Blocking simple and complex contagion by edge removal. In Proceedings of the ICDM. 399--408.Google Scholar
- Ravi Kumar, Jasmine Novak, Prabhakar Raghavan, and Andrew Tomkins. 2003. On the bursty evolution of blogspace. In WWW’03: Proceedings of the 12th International Conference on World Wide Web. ACM Press, New York, NY, USA, 568--576. DOI:http://dx.doi.org/10.1145/775152.775233 Google ScholarDigital Library
- T. Lappas, E. Terzi, D. Gunopoulos, and H. Mannila. 2010. Finding effectors in social networks. In Proceedings of the SIGKDD. 1059--1068. Google ScholarDigital Library
- Thomas Lengauer and Robert Endre Tarjan. 1979. A fast algorithm for finding dominators in a flowgraph. ACM Trans. Program. Lang. Syst. 1, 1 (January 1979), 121--141. Google ScholarDigital Library
- Jure Leskovec, Lada A. Adamic, and Bernardo A. Huberman. 2006. The dynamics of viral marketing. In EC’06: Proceedings of the 7th ACM Conference on Electronic Commerce. ACM Press, New York, NY, USA, 228--237. DOI:http://dx.doi.org/10.1145/1134707.1134732 Google ScholarDigital Library
- Jure Leskovec, Andreas Krause, Carlos Guestrin, Christos Faloutsos, Jeanne VanBriesen, and Natalie S. Glance. 2007a. Cost-effective outbreak detection in networks. In Proceedings of the KDD. 420--429. Google ScholarDigital Library
- Jure Leskovec, Mary McGlohon, Christos Faloutsos, Natalie Glance, and Matthew Hurst. 2007b. Cascading behavior in large blog graphs: Patterns and a model. In Society of Applied and Industrial Mathematics: Data Mining. 551--556.Google Scholar
- Shuyang Lin, Fengjiao Wang, Qingbo Hu, and Philip S. Yu. 2013. Extracting social events for learning better information diffusion models. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 365--373. Google ScholarDigital Library
- Nilly Madar, Tomer Kalisky, Reuven Cohen, Daniel ben Avraham, and Shlomo Havlin. 2004. Immunization and epidemic dynamics in complex networks. Eur. Phys. J. B 38, 2, 269--276.Google ScholarCross Ref
- Yasuko Matsubara, Yasushi Sakurai, B. Aditya Prakash, Lei Li, and Christos Faloutsos. 2012. Rise and fall patterns of information diffusion: Model and implications. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’12). 6--14. Google ScholarDigital Library
- A. G. McKendrick. 1925. Applications of mathematics to medical problems. In Proceedings of the Edinburgh Mathematical Society, Vol. 44. 98--130.Google ScholarCross Ref
- J. Medlock and A. P. Galvani. 2009. Optimizing influenza vaccine distribution. Science 325, 5948, 1705--1708.Google Scholar
- Lauren Ancel Meyers, M. E. J. Newman, and Babak Pourbohloul. 2006. Predicting epidemics on directed contact networks. J. Theoretical Biol. 240, 3, 400--418. DOI:http://dx.doi.org/DOI: 10.1016/j.jtbi.2005.10.004Google ScholarCross Ref
- James Moody and Douglas R. White. 2003. Social cohesion and embeddedness: a hierarchical conception of social groups. Am. Sociol. Rev. 68, 1, 39--54.Google ScholarCross Ref
- Fred Morstatter, Jürgen Pfeffer, Huan Liu, and Kathleen M. Carley. 2013. Is the sample good enough? Comparing data from Twitter’s streaming API with Twitter’s firehose. In Proceedings of ICWSM. 400--408.Google Scholar
- NDSSL. 2007. Synthetic data products for societal infrastructures and protopopulations: Data set 2.0. NDSSL-TR-07-003. Retreived from http://ndssl.vbi.vt.edu/Publications/ndssl-tr-07-003.pdf.Google Scholar
- Kenrad E. Nelson. 2005. Epidemiology of infectious disease: General principles. Infectious Disease Epidemiology Theory and Practice. Aspen Publishers, Gaithersburg, MD, 17--48.Google Scholar
- M. E. J. Newman. 2005. A measure of betweenness centrality based on random walks. Soc. Netw. 27, 1, 39--54.Google ScholarCross Ref
- Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. 1998. The PageRank Citation Ranking: Bringing Order to the Web. Technical Report. Stanford Digital Library Technologies Project. Retrived from http://dbpubs.stanford.edu/pub/1999-66 Paper SIDL-WP-1999-0120 (version of 11/11/1999).Google Scholar
- Romualdo Pastor-Satorras and Alessandro Vespignani. 2002. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E 65, 3, 1--4.Google ScholarCross Ref
- B. Aditya Prakash, Deepayan Chakrabarti, Michalis Faloutsos, Nicholas Valler, and Christos Faloutsos. 2011. Threshold conditions for arbitrary cascade models on arbitrary networks. In Proceedings of the ICDM. 549--575. Google ScholarDigital Library
- B. Aditya Prakash, Jilles Vreeken, and Christos Faloutsos. 2012. Spotting culprits in epidemics: How many and which ones?. In Proceedings of the ICDM. 11--20. Google ScholarDigital Library
- M. Richardson and P. Domingos. 2002. Mining knowledge-sharing sites for viral marketing. In Proceedings of the SIGKDD Conference. 61--70. Google ScholarDigital Library
- Kazumi Saito, Ryohei Nakano, and Masahiro Kimura. 2008. Prediction of information diffusion probabilities for independent cascade model. In Knowledge-Based Intelligent Information and Engineering Systems. Springer, 67--75. Google ScholarDigital Library
- C. Seshadhri, Tamara G. Kolda, and Ali Pinar. 2012. Community structure and scale-free collections of Erdős-Rényi graphs. Phys. Rev. E 85, 5, 1--9.Google ScholarCross Ref
- Devavrat Shah and Tauhid Zaman. 2011. Rumors in a network: Who’s the culprit? IEEE Trans. Inf. Theory 57, 8, 5163--5181. Google ScholarDigital Library
- Min-Zheng Shieh, Shi-Chun Tsai, and Ming-Chuan Yang. 2012. On the inapproximability of maximum intersection problems. Inf. Process. Lett. 112, 19 (Oct. 2012), 723--727. Google ScholarDigital Library
- Hanghang Tong, B. Aditya Prakash, Tina Eliassi-Rad, Michalis Faloutsos, and Christos Faloutsos. 2012. Gelling, and melting, large graphs by edge manipulation. In Proceedings of the 21st ACM International Conference on Information and Knowledge Management (CIKM’12). New York, NY, USA, 245--254. Google ScholarDigital Library
- Hanghang Tong, B. Aditya Prakash, Charalampos E. Tsourakakis, Tina Eliassi-Rad, Christos Faloutsos, and Duen Horng Chau. 2010. On the vulnerability of large graphs. In Proceedings of the ICDM. 1091--1096. Google ScholarDigital Library
- Staal A. Vinterbo. 2004. Privacy: A machine learning view. IEEE Trans. Knowl. Data Eng. 16, 8 (Aug. 2004), 939--948. Google ScholarDigital Library
- Yang Wang, Deepayan Chakrabarti, Chenxi Wang, and Christos Faloutsos. 2003. Epidemic spreading in real networks: An eigenvalue viewpoint. In Symposium on Reliable Distributed Systems. IEEE Computer Society Press, Los Alamitos, CA, 25--34.Google ScholarCross Ref
- Eduardo C. Xavier. 2012. A note on a maximum k-subset intersection problem. Inf. Process. Lett. 112, 12 (June 2012), 471--472. Google ScholarDigital Library
- Reza Yaesoubi and Ted Cohen. 2011. Dynamic health policies for controlling the spread of emerging infections: Influenza as an example. PLoS ONE 6, 9, 1--11.Google ScholarCross Ref
- Yao Zhang and B. Aditya Prakash. 2014. DAVA: Distributing vaccines over large networks under prior information. In Proceedings of the SIAM International Conference on Data Mining (SDM’14). 46--54.Google Scholar
Index Terms
- Data-Aware Vaccine Allocation Over Large Networks
Recommendations
Scalable Vaccine Distribution in Large Graphs given Uncertain Data
CIKM '14: Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge ManagementGiven an noisy or sampled snapshot of a network, like a contact-network or the blogosphere, in which an infection (or meme/virus) has been spreading for some time, what are the best nodes to immunize (vaccinate)? Manipulating graphs via node removal by ...
Modeling host-based detection and active worm containment
CNS '08: Proceedings of the 11th communications and networking simulation symposiumRecent advancements in Internet worms propagation techniques has generated interest in the development of appropriate defense techniques against such worms. Modeling the behaviour of worm defense techniques to better understand and measure their defense ...
Towards combating rumors in social networks: Models and metrics
Dynamic Networks and Knowledge DiscoveryRumor is a potentially harmful social phenomenon that has been observed in all human societies in all times. Social networking sites provide a platform for the rapid interchange of information and hence, for the rapid dissemination of unsubstantiated ...
Comments