Uniform multi-hop all-to-all optical routings in rings

Abstract

We consider all-to-all routing problem in an optical ring network that uses the wavelength-division multiplexing (WDM). Since one-hop, all-to-all optical routing in a WDM optical ring of n nodes needs w→ (Cn,I A,1) = [1/2|n2/4]] wavelengths which can be too large even for moderate values of n, we consider in this paper j-hop implementations of all-to-all routing in a WDM optical ring, j ≥ 2. ¿From among the possible routings we focus our attention on uniform routings, in which each node of the ring uses the same communication pattern. We show that there exists a uniform 2-hop, 3-hop, and 4-hop implementation of all-to-all routing that needs at most n+3/ 3 √n+16/5 + n/ 4,n/23√[n/4]+4/ 5, and n+16/24√[ n/4]+8 wavelengths, respectively. These values are within multiplicative constants of lower bounds. © Springer-Verlag Berlin Heidelberg 2000.