2 research outputs found
The covert set-cover problem with application to Network Discovery
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 within factor with high probability
using queries where is the input size.
We apply this technique to the network discovery problem that involves
certifying all the edges and non-edges of an unknown -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 -competitive Monte
Carlo randomized algorithm for the covert version of network discovery problem.
The previously best known algorithm has a competitive ratio of and therefore our result achieves an exponential improvement