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 $OPT$ within $O(\log N)$ factor with high probability using $O(OPT \cdot \log^2 N)$ queries where $N$ 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 $n$-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 $O(\log^2 n)$-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

Heat Transfer in Unsteady Squeezing Flow Between Parallel Plates

In this study, we investigated an unsteady MHD flow between parallel plates in the presence of viscous dissipation. The transformed governing equations are solved numerically using bvp5c Matlab package. The impact of different non-dimensional parameters on velocity and temperature profiles along with the local Nusselt number is discussed graphically. It is observed that the Nusselt number is a decreasing function of the radiation parameter and Hartmann number but it is an increasing function of squeeze number and Eckert number. Keywords:MHD, viscous dissipation, squeeze number, radiatio