Abstract
Challenges in social interaction networks are often modelled as graph theoretic problems. One such problem is to find a group of influential individuals of minimum size or the initial seed set in a social network, so that all the nodes in the network can be reached with only one hop from the seeds. This problem is equivalent to finding a minimum dominating set for the network. In this paper, we address a problem which is similar to finding minimum dominating set but differs in terms of number of hops needed to reach all the nodes. We have generalized the problem as k-hop dominating set problem, where a maximum of k hops will be allowed to spread the information among all the nodes of the graph. We show that the decision version of the k-hop dominating set problem is NP-complete. Results show that, in order to reach the same percentage of nodes in the network, if one extra hop is allowed then the cardinality of the seed set i.e. the number of influential nodes needed, is considerably reduced. Also, the experimental results show that the influential nodes can be characterized by their high betweenness values.
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References
Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256–278 (1974)
Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability pcp characterization of np. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC 1997, pp. 475–484 (1997)
Baker, B.S.: Approximation algorithms for np-complete problems on planar graphs. In: Proceedings of the 24th Annual Symposium on Foundations of Computer Science, SFCS 1983, pp. 265–273. IEEE Computer Society, Washington, DC (1983)
Hunt III, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: Nc-approximation schemes for np- and pspace-hard problems for geometric graphs. J. Algorithms 26(2), 238–274 (1998)
Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20, 374–387 (1998)
Bonneau, J., Anderson, J., Anderson, R., Stajano, F.: Eight friends are enough: Social graph approximation via public listings. In: Proceedings of the Second ACM EuroSys Workshop on Social Network Systems, SNS 2009, pp. 13–18. ACM, New York (2009)
Borgatti, S.P.: Identifying sets of key players in a social network. Comput. Math. Organ. Theory 12(1) (2006)
Eubank, S., Anil Kumar, V.S., Marathe, M.V., Srinivasan, A., Wang, N.: Structural and algorithmic aspects of massive social networks. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004 (2004)
Wang, F., Camacho, E., Xu, K.: Positive influence dominating set in online social networks. In: Du, D.-Z., Hu, X., Pardalos, P.M. (eds.) COCOA 2009. LNCS, vol. 5573, pp. 313–321. Springer, Heidelberg (2009)
Wang, F., Du, H., Camacho, E., Xu, K., Lee, W., Shi, Y., Shan, S.: On positive influence dominating sets in social networks. Theor. Comput. Sci. 412(3), 265–269 (2011)
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Basuchowdhuri, P., Majumder, S. (2014). Finding Influential Nodes in Social Networks Using Minimum k-Hop Dominating Set. In: Gupta, P., Zaroliagis, C. (eds) Applied Algorithms. ICAA 2014. Lecture Notes in Computer Science, vol 8321. Springer, Cham. https://doi.org/10.1007/978-3-319-04126-1_12
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DOI: https://doi.org/10.1007/978-3-319-04126-1_12
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