STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Robust monitoring of link delays and faults in IP networks
IEEE/ACM Transactions on Networking (TON)
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
network discovery and verification
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Network Discovery and Verification
IEEE Journal on Selected Areas in Communications
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We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We want to find a small set-cover using a minimal number of such queries. We present a Monte Carlo randomized algorithm that approximates an optimal set-cover of size OPT within O(logN) factor with high probability using O( OPT ·log2N ) queries where N is the number of elements in the universal set. We apply this technique to the network discovery problem that involves certifying all the edges and non-edges of an unknown n-vertices graph based on layered-graph queries from a minimal number of vertices. By reducing it to the covert set-cover problem we present an O(log2n)-competitive Monte Carlo randomized algorithm for the covert version of network discovery problem. The previously best known algorithm has a competitive ratio of $\Omega ( \sqrt{n\log n} )$ and therefore our result achieves an exponential improvement.