Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exploring networks with traceroute-like probes: theory and simulations
Theoretical Computer Science - Complex networks
Approximability of identifying codes and locating--dominating codes
Information Processing Letters
Discovery of network properties with all-shortest-paths queries
Theoretical Computer Science
Optimal query complexity bounds for finding graphs
Artificial Intelligence
Reconstructing weighted graphs with minimal query complexity
Theoretical Computer Science
Network Discovery and Verification
IEEE Journal on Selected Areas in Communications
Approximate discovery of random graphs
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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We address the problem of verifying the accuracy of a map of a network by making as few measurements as possible on its nodes. This task can be formalized as an optimization problem that, given a graph G = (V,E), and a query model specifying the information returned by a query at a node, asks for finding a minimum-size subset of nodes of G to be queried so as to univocally identify G. This problem has been faced w.r.t. a couple of query models assuming that a node had some global knowledge about the network. Here, we propose a new query model based on the local knowledge a node instead usually has. Quite naturally, we assume that a query at a given node returns the associated routing table, i.e., a set of entries which provides, for each destination node, a corresponding (set of) first-hop node(s) along an underlying shortest path. First, we show that any network of n nodes needs Ω(log log n) queries to be verified. Then, we prove that there is no o(log n)-approximation algorithm for the problem, unless P = NP, even for networks of diameter 2. On the positive side, we provide an O(log n)-approximation algorithm to verify a network of diameter 2, and we give exact polynomial-time algorithms for paths, trees, and cycles of even length.