Abstract
Motivated by applications in social networks, a new type of dominating set has been studied in the literature. In this paper, we present results regarding the complexity and approximation in general graphs.
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Calinescu, G., Chekuri, C., Pal, M., Vondrak, J.: Maximizing a submodular set function subject to a matroid constraint. In: Proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization (IPCO 2007), pp. 182–196 (2007)
Du, D.-Z., Graham, R.L., Pardalos, P.M., Wan, P.-J., Wu, W., Zhao, W.: Analysis of greedy approximations with nonsubmodular potential functions. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Dicrete Algorithms (SODA). San Francisco, USA, Jan 20–22, pp. 167–175 (2008)
Du D.-Z., Gao B., Wu W.: A special case for subset interconnection designs. Discret. Appl. Math. 78, 51–60 (1997)
Du, D.-Z., Ko, K.-I., Hu, X.: Design and Analysis of Approximation Algorithms, Lecture Notes (2008)
Du D.-Z., Ko K.-I.: Theory of Computational Complexity. Wiley, New York (2000)
Feige U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–652 (1998)
Gao X., Wang Y., Li X., Wu W.: Analysis on theoretical bonds for approximating dominating set problems. Discret. Math. Algorithms Appl. 1(1), 71–84 (2009)
Li D., Liu L., Yang H.: Minimum connected r-hop k-dominating set in wireless networks. Discret. Math. Algorithms Appl. 1(1), 45–57 (2009)
Ruan L., Du H., Jia X., Wu W., Li Y., Ko K.: A greedy approximation for minimum connected dominating sets. Theor. Comput. Sci. 329, 325–330 (2004)
Shioura A.: On the pipage rounding algorithm for submodular function maximization: a view from discrete convex analysis. Discret. Math. Algorithms Appl. 1(1), 1–13 (2009)
Wang W., Kim D., Sohaee N., Ma C., Wu W.: A PTAS for minimum d-hop underwater sink placement problem in 2-D underwater sensor networks. Discret. Math. Algorithms Appl. 1(2), 283–289 (2009)
Wang W., Kim D., Willson J., Thuraisingham B., Wu W.: A better approximation for minimum average routing path clustering problem in 2-D underwater sensor networks. Discret. Math. Algorithms Appl. 1(2), 175–191 (2009)
Wolsey L.A.: An analysis of the greedy algorithm for submodular set covering problem. Combinatorica 2(4), 385–393 (1982)
Zou, F., Zhang, Z., Wu, W.: Latency-bounded minimum influential node selection in social networks. In: Proceedings of Workshop on Social Networks, Applications, and Systems. Boston, Aug 16 (2009)
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This research was jointly supported by MEST, Korea under WCU (R33-2008-000-10044-0), by the KOSEF grant funded by the Korea government (MEST) (No. R01- 2007-000-11203-0), by KRF Grant funded by (KRF-2008- 314-D00354), and by MKE, Korea under ITRC IITA-2009- (C1090-0902-0046) and IITA-2009-(C1090-0902-0007).
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Zhu, X., Yu, J., Lee, W. et al. New dominating sets in social networks. J Glob Optim 48, 633–642 (2010). https://doi.org/10.1007/s10898-009-9511-2
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DOI: https://doi.org/10.1007/s10898-009-9511-2