Abstract
For any non-negative integer K, a K-observer P of a network N is a set of nodes in N such that each message, that travels at least K hops in N, is handled (and so observed) by at least one node in P. A K-observer P of a network N is minimum iff the number of nodes in P is less than or equal the number of nodes in every K-observer of N. The nodes in a minimum K-observer of a network N can be used to monitor the message traffic in network N, detect denial-of-service attacks, and act as firewalls to identify and discard attack messages. This paper considers the problem of constructing a minimum K-observer for any given network. We show that the problem is NP-hard for general networks, and give linear-time algorithms for constructing minimum or near-minimum K-observers for special classes of networks: trees, rings, L-rings, and large grids.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Acharya, H.B., Joshi, A., Gouda, M.G.: Firewall modules and modular firewalls. In: Proceedings of the 18TH IEEE International Conference on Network Protocols, ICNP 2010 (2010)
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: Proceedings of the 3rd ACM International Symposium on Mobile ad Hoc Networking & Computing, MobiHoc 2002, pp. 157–164. ACM, New York (2002)
Armbruster, B., Smith, J.C., Park, K.: A packet filter placement problem with application to defense against spoofed denial of service attacks. European Journal of Operational Research (2007)
Breslau, L., Diakonikolas, I., Duffield, N., Gu, Y., Hajiaghayi, M., Johnson, D.S., Karloff, H., Resende, M., Sen, S.: Disjoint-path facility location: Theory and practice. In: Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments, ALENEX (2011)
Calvert, K., Doar, M.B., Nexion, A., Zegura, E.W.: Modeling internet topology. IEEE Communications Magazine 35, 160–163 (1997)
Chen, B., Jamieson, K., Balakrishnan, H., Morris, R.: Span: an energy-efficient coordination algorithm for topology maintenance in ad hoc wireless networks. Wirel. Netw. 8, 481–494 (2002)
Chvátal, V.: A combinatorial theorem in plane geometry. Journal of Combinatorial Theory, Series B, 39–41 (1975)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM 1999, pp. 251–262. ACM, New York (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Huang, C.-F., Tseng, Y.-C.: The coverage problem in a wireless sensor network. In: Proceedings of the 2nd ACM International Conference on Wireless Sensor Networks and Applications, WSNA 2003, pp. 115–121. ACM, New York (2003)
Karp, R.: Reducibility among combinatorial problems. In: Miller, R., Thatcher, J. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Lee, S.-J., Su, W., Gerla, M.: Wireless ad hoc multicast routing with mobility prediction. Mob. Netw. Appl. 6, 351–360 (2001)
Meguerdichian, S., Koushanfar, F., Potkonjak, M., Srivastava, M.B.: Coverage problems in wireless ad-hoc sensor networks. In: Prodeedings of IEEE INFOCOM, pp. 1380–1387 (2001)
Qiu, L., Padmanabhan, V.N., Voelker, G.M.: On the placement of web server replicas. In: Proceedings of IEEE INFOCOM, pp. 1587–1596 (2001)
Qiu, T., Ji, L., Pei, D., Wang, J., Xu, J.: Towerdefense: Deployment strategies for battling against ip prefix hijacking. In: Proceedings of the 18th IEEE International Conference on Network Protocols, ICNP (October 2010)
Roy, S., Pucha, H., Zhang, Z., Hu, Y.C., Qiu, L.: Overlay node placement: Analysis, algorithms and impact on applications. In: International Conference on Distributed Computing Systems, p. 53 (2007)
Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. Mob. Netw. Appl. 9, 141–149 (2004)
Weber, A.: Theory of the Location of Industries. The University of Chicago Press, Chicago (1909)
Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, DIALM 1999, pp. 7–14. ACM, New York (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Acharya, H.B., Choi, T., Bazzi, R.A., Gouda, M.G. (2011). The K-Observer Problem in Computer Networks. In: Défago, X., Petit, F., Villain, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2011. Lecture Notes in Computer Science, vol 6976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24550-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-24550-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24549-7
Online ISBN: 978-3-642-24550-3
eBook Packages: Computer ScienceComputer Science (R0)