Capture on grids and tori with different number of Cops

This paper is a contribution to the classical cops and robber problem on a graph, directed to two-dimensional grids and tori. We apply some new concepts for solving the problem on grids and apply these concepts to give a new algorithm for the capture on tori. Then we consider using any number k of cops, give efficient algorithms for this case yielding a capture time t_k and compute the minimum value of k needed for any given capture time. We introduce the concept of work, w_k= k t_k of an algorithm and study a possible speed-up using larger teams of cops.