Abstract
Minimum m-connected k-dominating set problem is as follows: Given a graph G=(V,E) and two natural numbers m and k, find a subset S⊆V of minimal size such that every vertex in V∖S is adjacent to at least k vertices in S and the induced graph of S is m-connected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of fault-tolerant virtual backbone for wireless sensor networks. We propose two approximation algorithms with constant performance ratios for m≤2. We also discuss how to design approximation algorithms for the problem with arbitrarily large m.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alzoubi KM, Wan P-J, Frieder O (2002) Distributed heuristics for connected dominating sets in wireless ad hoc networks. J Commun Netw 4(1):22–29
Bredin JL, Demaine ED, Hajiaghayi M, Rus D (2005) Deploying sensor networks with guaranteed capacity and fault tolerance. In: Proceedings of the 6th ACM international symposium on mobile ad hoc networking and computing (MobiHoc), pp 309–319
Dai F, Wu J (2006) On constructing k-connected k-dominating set in wireless ad hoc and sensor networks. J Parallel Distrib Comput 66(7):947–958
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York
Koskinen H, Karvo J, Apilo O (2005) On improving connectivity of static ad-hoc networks by adding nodes. In: Proceedings of the 4th annual Mediterranean workshop on ad hoc networks (Med-Hoc-Net), pp 169–178
Kuhn F, Moscibroda T, Wattenhofer R (2006) Fault-tolerant clustering in ad hoc and sensor networks. In: Proceedings 26th international conference on distributed computing systems (ICDCS)
Li YS, Thai MT, Wang F, Yi C-W, Wan P-J, Du D-Z (2005) On greedy construction of connected dominating sets in wireless networks. Wiley J Wirel Commun Mobile Comput 5(8):927–932
Shang W-P, Yao F, Wan P-J, Hu X-D (2007) Algorithms for minimum m-connected k-tuple dominating set problem. Theor Comput Sci 381(1–3):241–247
Sinha P, Sivakumar R, Bharghavan V (2001) Enhancing ad hoc routing with dynamic virtual infrastructures. In: Proceedings of the 20th annual joint conference of the IEEE computer and communications societies, vol 3, pp 1763–1772
Tarjan R (1972) Depth first search and linear graph algorithms. SIAM J Comput 1(2):146–160
Wan P-J, Alzoubi KM, Frieder O (2004) Distributed construction of connected dominating set in wireless ad hoc networks. Mobile Netw Appl 9(2):141–149
Wang F, Thai T, Du DZ (2007) On the construction of 2-connected virtual backbone in wireless networks. IEEE Trans Wirel Commun (to appear)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported in part by the Research Grants Council of Hong Kong under Grant No. CityU 1165/04E, the National Natural Science Foundation of China under Grant No. 70221001, 10531070 and 10771209.
Rights and permissions
About this article
Cite this article
Shang, W., Yao, F., Wan, P. et al. On minimum m-connected k-dominating set problem in unit disc graphs. J Comb Optim 16, 99–106 (2008). https://doi.org/10.1007/s10878-007-9124-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-007-9124-y