Browse > Article
http://dx.doi.org/10.7737/JKORMS.2014.39.2.131

The Challenge of Managing Customer Networks under Change : Proving the Complexity of the Inverse Dominating Set Problem  

Chung, Yerim (School of Business, Yonsei University)
Park, Sunju (School of Business, Yonsei University)
Chung, Seungwha (School of Business, Yonsei University)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.39, no.2, 2014 , pp. 131-140 More about this Journal
Abstract
Customer networks go through constant changes. They may expand or shrink once they are formed. In dynamic environments, it is a critical corporate challenge to identify and manage influential customer groups in a cost effective way. In this context, we apply inverse optimization theory to suggest an efficient method to manage customer networks. In this paper, we assume that there exists a subset of nodes that might have a large effect on the network and that the network can be modified via some strategic actions. Rather than making efforts to find influential nodes whenever the network changes, we focus on a subset of selective nodes and perturb as little as possible the interaction between nodes in order to make the selected nodes influential in the given network. We define the following problem based on the inverse optimization. Given a graph and a prescribed node subset, the objective is to modify the structure of the given graph so that the fixed subset of nodes becomes a minimum dominating set in the modified graph and the cost for modification is minimum under a fixed norm. We call this problem the inverse dominating set problem and investigate its computational complexity.
Keywords
Customer Network; Inverse Optimization; Dominating Set; Computational Complexity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Domingos, P. and M. Richardson, "Mining the network value of customers," Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, pp.57-66, ACM, New York, 2001.
2 Chung, Y. and M. Demange, "The 0-1 inverse maximum stable set problem," Discrete Applied Mathematics, Vol.156, No.13(2008), pp.2501-2516.   DOI
3 Chung, Y. and M. Demange, "On inverse traveling salesman problems," 4OR-A Quarterly Journal of Operations Research, Vol.10(2012), pp.193-209.   DOI
4 Chung, Y., "Inverse bin-packing number problems : Hardness and approximation results," Management Science and Financial Engineering, Vol.18, No.2(2012), pp.1-4.
5 Garey, M.R. and D.S. Johnson, Computers and intractability : a guide to the theory of NP-completeness, Freeman, San Francisco, 1979.
6 Wan, P.-J., K.M. Alzoubi, and O. Frieder, "Distributed construction of connected dominating set in wireless ad hoc networks," Mobile Networks and Applications, Vol.9 (2004), pp.141-149.   DOI
7 Kempe, D., J. Kleinberg, and E. Tardos, "Maximizing the spread of influence through a social network," Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2003), pp.137-146.
8 Kimmel, A.J., Connecting with consumers: Marketing for new marketplace realities, Oxford University Press, 2010.
9 Rogers, D.L. The network is your customer : five strategies to thrive in a digital age, Yale University Press, 2010.
10 Wu, J. and H. Li, "A dominating-set-based routing scheme in ad hoc wireless networks," Telecommunication Systems, Vol.18, No.1-3 (2001), pp.13-36.   DOI
11 Wuyts, S., M.G. Dekimpe, E. Gijsbrechts, and R. Pieters, The connected customer : The changing nature of customer and business market, Routledge, 2010.
12 Yang, C., J. Zhang and Z. Ma, "Inverse maximum flow and minimum cut problems," Optimization, Vol.40(2007), pp.147-170.
13 Yu, J., N. Wang, G. Wang, and D. Yu, "Connected dominating sets in wireless ad hoc and sensor networks-A comprehensive survey," Computer Communications, Vol.36, No.2(2013), pp.121-134.   DOI
14 Zhang, J. and M.C. Cai, "Inverse problem of minimum cuts," Mathematical Methods of Operations Research, Vol.47, No.1(1998), pp.51-58.   DOI
15 Zhang, J. and Z. Liu, "Calculating some inverse linear programming problem," Journal of Computational and Applied Mathematics, Vol.72(1996), pp.261-273.   DOI
16 이유재, 이지영, "브랜드 동일시, 브랜드 감정, 브랜드 로열티의 관계에 대한 연구", 광고연구, 제65호(2004) pp.143-162.
17 이현정, "고객충성도, 신뢰와 애착으로 높여라", [LG주간경제], 2006. 4. 19.
18 Ahuja, R.K. and J.B. Orlin, "Inverse optimization," Operations Research, Vol.49, No.5 (2001), pp.771-783.   DOI
19 Burton, D. and Ph.L. Toint, "On an instance of the inverse shortest paths problem," Mathematical Programming, Vol.53(1992), pp.45-61.   DOI
20 Guille, A., H. Hacid, C. Favre, and D.A. Zighed, "Information diffusion in online social networks : A survey," ACM SIGMOD Record, Vol.42, No.2(2013), pp.17-28.   DOI
21 Zhang, J., X.G. Yang, and M.C. Cai, "The complexity analysis of the inverse center location problem," Journal of Global Optimization, Vol.15, No.2(1999), pp.213-218.   DOI
22 Heuberger, C., "Inverse combinatorial optimization : A survey on problems, methods, and results," Journal of Combinatorial Optimization, Vol.8, No.3(2004), pp.329-361.   DOI