Efficient access to optical bandwidth wavelength routing on directed fiber trees, rings, and trees of rings

We address efficient access to bandwidth in WDM (wavelength division multiplexing) optical networks. We consider tree topologies, ring topologies, as well as trees of rings. These are topologies of concrete practical relevance for which undirected underlying graph models have been studied before by P. Raghavan and E. Upfal (1993). As opposed to previous studies (A. Aggarwal et al., 1993; R. Pankaj, 1992; P. Raghavan and E. Upfal, 1993), we consider directed graph models. Directedness of fiber links is dictated by physical directedness of optical amplifiers. For trees, we give a polynomial time routing algorithm that satisfies requests of maximum load L_max per fiber link using no more than 15L_max/8⩽15OPT/8 optical wavelengths. This improves a 2L_max scheme that is implicit by P. Raghavan and E. Upfal by extending their undirected methods to our directed model. Alternatively stated, for fixed W wavelength technology, we can load the network up to L,, 8W/15 rather than W/2. In engineering terms, this is a so called “6.66% increase of bandwidth” and it is considered substantial. For rings, the approximation factor is 2OPT. For trees of rings, the approximation factor is 15OPT/4. Technically, optical routing requirements give rise to novel coloring paradigms. Our algorithms involve matchings and multicolored alternating cycles, combined with detailed potential and averaging analysis