Abstract
Graph burning is a deterministic, discrete-time process that can be used to model how influence or contagion spreads in a graph. In the graph burning process, each node starts as dormant, and becomes informed/burned over time; when a node is burned, it remains burned until the end of the process. In each round, one can burn a new node (source of fire) in the network. Once a node is burned in round t, in round \(t+1\), each of its dormant neighbors becomes burned. The process ends when all nodes are burned; the goal is to minimize the number of rounds. We study a variation of graph burning in order to model spreading processes in community-based networks. With respect to a specific piece of information, a community is satisfied when this information reaches at least a prescribed number of its members. Specifically, we consider the problem of identifying a minimum length sequence of nodes that, according to a graph burning process, allows to satisfy all the communities of the network. We investigate this NP-hard problem from an approximation point of view, showing both a lower bound and a matching upper bound. We also investigate the case when the number of communities is constant and show how to solve the problem with a constant approximation factor. Moreover, we consider the problem of maximizing the number of satisfied groups, given a budget k on the number of rounds.
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Notes
- 1.
For any integer a, we denote by [a] the set {1, 2, ..., a}.
References
Ackerman, E., Ben-Zwi, O., Wolfovitz, G.: Combinatorial model and bounds for target set selection. Theor. Comp. Sci. 411(44–46), 4017–4022 (2010)
Arora, S., Lund, C.: Hardness of approximation. In: Hochbaum, Ed. D. (ed.) Approximation Algorithms for NP-Hard Problems, pp. 399–446 PWS Publishers (1995)
Bandyapadhyay, S., Inamdar, T., Pai, S., Varadarajan, K.: A constant approximation for colorful k-center. arXiv:1907.08906v1 (2019)
Ben-Zwi, O., Hermelin, D., Lokshtanov, D., Newman, I.: Treewidth governs the complexity of target set selection. Discrete Optim. 8(1), 87–96 (2011)
Bonato, A.: A survey of graph burning. Contr. Discret. Math. 16, 185–197 (2021)
Bonato, A., Kamali, S.: Approximation algorithms for graph burning. In: Gopal, T.V., Watada, J. (eds.) TAMC 2019. LNCS, vol. 11436, pp. 74–92. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14812-6_6
Chekuri, C., Kumar, A.: Maximum coverage problem with group budget constraints and applications. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) APPROX/RANDOM -2004. LNCS, vol. 3122, pp. 72–83. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27821-4_7
Chen, W., Lakshmanan, L.V.S., Castillo, C.: Information and influence propagation in social networks. In: Synthesis Lectures on Data Management, vol. 5.4 (2013)
Chopin, M., Nichterlein, A., Niedermeier, R., Weller, M.: Constant thresholds can make target set selection tractable. Theory Comput. Syst. 55(1), 61–83 (2014). https://doi.org/10.1007/s00224-013-9499-3
Cicalese, F., Cordasco, G., Gargano, L., Milanic, M., Vaccaro, U.: Latency-bounded target set selection in social networks. Theor. Comp. Sci. 535, 1–15 (2014)
Coja-Oghlan, A., Feige, U., Krivelevich, M., Reichman, D.: Contagious sets in expanders. In: Proceedings of SODA, pp. 1953–1987 (2015)
Cordasco, G., Gargano, L., Rescigno, A.A.: Influence propagation over large scale social networks. In: Proceedings of ASONAM, pp. 1531–1538 (2015)
Cicalese, F., Cordasco, G., Gargano, L., Milanic, M., Peters, J., Vaccaro, U.: Spread of influence in weighted networks under time and budget constraints. Theor. Comp. Sci. 586, 40–58 (2015)
Cordasco, G., Gargano, L., Rescigno, A.A.: On finding small sets that influence large networks. Soc. Netw. Anal. Min. 6, 1–20 (2016)
Cordasco, G., Gargano, L., Rescigno, A.A., Vaccaro, U.: Evangelism in social networks: algorithms and complexity. Networks 71(4), 346–357 (2018)
Cordasco, G., Gargano, L., Mecchia, M., Rescigno, A.A., Vaccaro, U.: Discovering small target sets in social networks: a fast and effective algorithm. Algorithmica 80, 1804–1833 (2018). https://doi.org/10.1007/s00453-017-0390-5
Cordasco, G., Gargano, L., Rescigno, A.A.: Active influence spreading in social networks. Theor. Comp. Sci. 764, 15–29 (2019)
Cordasco, G., et al.: Whom to befriend to influence people. Theor. Comp. Sci. 810, 26–42 (2020)
Cordasco, G., Gargano, L., Peters, J.G., Rescigno, A.A., Vaccaro, U.: Fast and frugal targeting with incentives. Theor. Comp. Sci. 812, 62–79 (2020)
Dinh, T.N., Zhang, H., Nguyen, D.T., Thai, M.T.: Cost-effective viral marketing for time-critical campaigns in large-scale social networks. IEEE Trans. Net. 22, 2001–2011 (2014)
Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected world. Cambridge University Press, Cambridge (2010)
Gargano, L., Hell, P., Peters, J.G., Vaccaro, U.: Influence diffusion in social networks under time window constraints. Theor. Comp. Sci. 584(C), 53–66 (2015)
Jia, X., Sheth, K., Svensson, O.: Fair colorful k-center clustering. arXiv:2007.04059v1 (2020)
Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of KDD 2003 (2003)
Lev, B., Soyster, A.L.: Integer programming with bounded variables via canonical separation. J. Oper. Res. Soc. 29(5), 477–488 (1978)
Reddy, T.V.T., Rangan, C.P.: Variants of spreading messages. J. Graph Algorithms Appl. 15(5), 683–699 (2011)
Shakarian, P., Eyre, S., Paulo, D.: A scalable heuristic for viral marketing under the tipping model. Soc. Netw. Anal. Min. 3(4), 1225–1248 (2013). https://doi.org/10.1007/s13278-013-0135-7
Zhu, J., Ghosh, S., Wu, W.: Group influence maximization problem in social networks. IEEE Trans. Comput. Soc. Syst. 6(6), 1156–1164 (2019)
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Cordasco, G., Gargano, L., Rescigno, A.A. (2023). Groups Burning: Analyzing Spreading Processes in Community-Based Networks. In: Lin, CC., Lin, B.M.T., Liotta, G. (eds) WALCOM: Algorithms and Computation. WALCOM 2023. Lecture Notes in Computer Science, vol 13973. Springer, Cham. https://doi.org/10.1007/978-3-031-27051-2_28
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