The Generalized Regenerator Location Problem

In an optical network a signal can only travel a maximum distance dmax before its quality deteriorates to the point that it must be regenerated by installing regenerators at nodes of the network. As the cost of a regenerator is high, we wish to deploy as few regenerators as possible in the network, while ensuring all nodes can communicate with each other. In this paper we introduce the generalized regenerator location problem (GRLP) in which we are given a set S of nodes that corresponds to candidate locations for regenerators, and a set T of nodes that must communicate with each other. If S = T = N, we obtain the regenerator location problem (RLP), which we have studied previously and shown to be NP-complete. Our solution procedure to the RLP is based on its equivalence to the maximum leaf spanning tree problem (MLSTP). Unfortunately, this equivalence does not apply to the GRLP, nor do the procedures developed previously for the RLP. To solve the GRLP, we propose reduction procedures, two construction he...