The problem of efficiently monitoring the network flow is regarded as the one to find out the minimum weighted weak vertex cover set for a given graph G = (V, E) with weight func...
We study the partial vertex cover problem. Given a graph G = (V, E), a weight function w : V → R+ , and an integer s, our goal is to cover all but s edges, by picking a set of v...
For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph...
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the Vertex Cover problem whose approximation ratio is bounded by a constant l...
We consider a wireless sensor network in which each sensor is able to transmit within a disk of radius one. We show with elementary techniques that there exists a constant c such t...