On the Complexity of the Regenerator Location Problem - Treewidth and Other Parameters

Abstract

We deal with the Regenerator Location Problem in optical networks. We are given a network G = (V, E), and a set ${\cal Q}$ of communication requests between pairs of terminals in V. We investigate two variations: one in which we are given a routing ${\cal P}$ of the requests in ${\cal Q}$, and one in which we are required to find also the routing. In both cases, each path in ${\cal P}$ must contain a regenerator after every d edges in order to deal with loss of signal quality for some d > 0. The goal is to minimize the number of vertices that contain regenerators used by the solution. Both variations of the problem are $\textsc{NP-hard}$ in the general case. In this work we investigate the parameterized complexity of the problem. We introduce several fixed parameter tractability results and polynomial algorithms for fixed parameter values, as well as several $\textsc{NP-hardness}$ results. The parameters under consideration are the treewidth of the input graph, the sizes d and $|{{\cal Q}}|$ and the vertex load, i.e. the maximum number of paths passing through any vertex.