Broadcast in sparse conversion optical networks using fewest converters

Wavelengths and converters are shared by communication requests in optical networks. When a message goes through a node without a converter, the outgoing wavelength must be the same as the incoming one. This constraint can be removed if the node uses a converter. Hence, the usage of converters increases the utilization of wavelengths and allows more communication requests to succeed. Since converters are expensive, we consider sparse conversion networks, where only some specified nodes have converters. Moreover, since the usage of converters induces delays, we should minimize the use of available converters. The Converters Usage Problem (CUP) is to use a minimum number of converter so that each node can send messages to all the others (broadcasting). In this dissertation, we study the CUP in sparse conversion networks. We design a linear algorithm to find a wavelength assignment in tree networks such that, with the usage of a minimum number of available converters, every node can send messages to all the others. This is a generalization of [35], where each node has a converter. Our algorithm can assign wavelengths efficiently and effectively for one-to-one, multicast, and broadcast communication requests. A converter wavelength-dominates a node if there is a uniform wavelength path between them. The Minimal Wavelength Dominating Set Problem (MWDSP) is to locate a minimum number of converters so that all the other nodes in the network are wavelength-dominated. We use a linear complexity dynamic programming algorithm to solve the MWDSP for networks with bounded treewidth. One such solution provides a low bound for the optimal solution to the CUP

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

A Low Bound for Broadcast in Optical Networks of Bounded Treewidth Using Fewest Converters

Wavelengths and converters are shared by communication requests in optical networks. The usage of converters increases the utilization of wavelengths and allows more requests to succeed. The Converters Usage Problem (CUP) is to determine the minimum number of converter so that each node can send messages to all the others (broadcasting). In this paper, we study the CUP in sparse conversion networks with bounded treewidth. A converter wavelength-dominates a node if there is a uniform wavelength path between them. The Minimal Wavelength Dominating Set Problem (MWDSP) is to locate the minimum number of converters so that all the other nodes in the network are wavelength-dominated. We use a linear complexity dynamic programming algorithm to solve the MWDSP for networks with bounded treewidth. One such solution provides a low bound for the optimal solution to the CUP. © 2007 IEEE