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 guaranteed to reach (and so can be 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 no more than 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 and collect traffic statistics, detect patterns of denial-of-service attacks when they occur in N, and act as firewalls to identify and discard attack messages from network N. In this paper, we consider 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.
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Acharya, H.B., Choi, T., Bazzi, R.A. et al. The K-observer problem in computer networks. Netw.Sci. 1, 15–22 (2012). https://doi.org/10.1007/s13119-011-0002-7
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DOI: https://doi.org/10.1007/s13119-011-0002-7