The K-observer problem in computer networks

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.

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