Min-Max Coverage in Multi-interface Networks
We consider devices equipped with multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider the problem of establishing the connections defined by a network G = (V,E) while keeping as low as possible the maximum cost set of active interfaces at the single nodes. Nodes V represent the devices, edges E represent the connections that must be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges. We prove that the problem is NP-hard for any fixed Δ ≥ 5 and k ≥ 16, with Δ being the maximum degree, and k being the number of different interfaces among the network. We also show that the problem cannot be approximated within Ω(ln Δ). We then provide a general approximation algorithm which guarantees a factor of O((1 + b)ln (Δ)), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented.
Unable to display preview. Download preview PDF.
- 5.Caporuscio, M., Charlet, D., Issarny, V., Navarra, A.: Energetic Performance of Service-oriented Multi-radio Networks: Issues and Perspectives.. In: 6th Int. Workshop on Software and Performance (WOSP), pp. 42–45. ACM Press, New York (2007)Google Scholar
- 6.Cavalcanti, D., Gossain, H., Agrawal, D.: Connectivity in multi-radio, multi-channel heterogeneous ad hoc networks. In: IEEE 16th Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC), pp. 1322–1326. IEEE, Los Alamitos (2005)Google Scholar
- 8.D’Angelo, G., Di Stefano, G., Navarra, A.: Minimizing the Maximum Duty for Connectivity in Multi-Interface Networks. In: Zhong, F. (ed.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 254–267. Springer, Heidelberg (2010)Google Scholar
- 9.Draves, R., Padhye, J., Zill, B.: Routing in multi-radio, multi-hop wireless mesh networks. In: 10th Annual International Conference on Mobile Computing and Networking (MobiCom), pp. 114–128. ACM, New York (2004)Google Scholar
- 10.Faragó, A., Basagni, S.: The effect of multi-radio nodes on network connectivity—a graph theoretic analysis. In: IEEE Int. Workshop on Wireless Distributed Networks (WDM). IEEE, Los Alamitos (2008)Google Scholar