Covering based rough sets are a generalization of classical rough sets, in which the traditional partition of the universe induced by an equivalence relation is replaced by a covering. Many definitions have been proposed for the lower and upper approximations within this setting. In this paper, we recall the most important ones and organize them into sixteen dual pairs. Then, to provide more in...

A perfect matching covering of a graph G is a set of perfect matchings of G such that every edge of G is contained in at least one member of it. Berge conjectured that every bridgeless cubic graph admits a perfect matching covering of order at most 5 (we call such a collection of perfect matchings a Berge covering of G). A cubic graph G is called a Kotzig graph if G has a 3-edge-coloring such t...

Many infectious diseases are caused by viral infections, and in particular by RNA viruses such as MERS, Ebola and Zika. To understand viral disease, detection and identification of these viruses are essential. Although PCR is widely used for rapid virus identification due to its low cost and high sensitivity and specificity, very few online database resources have compiled PCR primers for RNA v...

a paper-pot transplanter was designed, developed and evaluated in the field by transplanting sugar beet seedlings grown in paper pots. a ground-driven counter wheel equipped with an infra-red sensor measures the traveled distance and sends the corresponding signals to a micro-controller. a step motor controlled by the micro-controller turns the driving shaft of the paper-pot metering mechanism ...

Given two 3-uniform hypergraphs F and G = (V,E), we say that G has an F -covering if we can cover V with copies of F . The minimum codegree of G is the largest integer d such that every pair of vertices from V is contained in at least d triples from E. Define c2(n, F ) to be the largest minimum codegree among all n-vertex 3-graphs G that contain no F -covering. Determining c2(n, F ) is a natura...

We consider combinatorial problems motivated by sensor networks for beacon-based point-to-point routing and covering. A beacon b is a point that can be activated to effect a ‘magnetic pull’ toward itself everywhere in a polygonal domain P . The routing problem asks how many beacons are required to route between any pair of points in a polygonal domain P . In simple polygons with n vertices we s...

We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each...