Minimizing maximum fiber requirement in optical networks

Abstract

We study wavelength assignment in an optical network where each fiber has a fixed capacity of wavelengths. Given demand routes, we aim to minimize the maximum ratio between the number of fibers deployed on a link e and the number of fibers required on the same link e when wavelength assignment is allowed to be fractional. Our main results are negative ones. We show that there is no constant-factor approximation unless NP⊆ ZPP. In addition, unless NP ⊆ ZPTIME(n polylog n ) we show that there is no log approximation for any ∈ (0, 1) and no log m approximation for any ∈ (0, 0.5) where m is the number of links in the network. Our analysis is based on the hardness of approximating the chromatic numbers. On the positive side, we present algorithms with approximation ratios O(log m + log ), O(log D max + log ) and O(D max ) respectively, where D max is the length of the longest path.

On a Noncooperative Model for Wavelength Assignment in Multifiber Optical Networks

“…To this end, several optimization problems have been defined and studied, the objective being to minimize either the maximum fiber multiplicity per edge [1,2,3] or the sum of these maximum multiplicities over all edges of the graph [4,5,6]; in another scenario the allowed fiber multiplicity per edge is given and the goal is to minimize the number of wavelengths needed [7,8,5].…”

“…Minimizing this quantity is particularly important in cases where fibers are hired or sold as a whole, hence the maximum number of fibers needed on an edge determines the total cost; further motivation can be found in papers that address the corresponding optimization problem (see e.g. [1,2,3]). Here we focus on situations where routing is unique (acyclic topologies) or pre-determined-as happens in many practical settings, for example in cases where there are specific routing constraints such as a requirement to use lightpaths that have been set in advance, or shortest path routing.…”