Minimizing the Number of ADMsWith and Without Traffic Grooming: Complexity and Approximability

Abstract

A relatively new optimization criterion in studies of optical networks is that of minimizing the total number of ADMs. In these networks each given lightpath uses one ADM device at each of its two endpoints, and it is assigned a color, so that at most g lightpaths of the same color can share an edge. Lightpaths of the same color that share an endpoint can use a common ADM at that endpoint. We discuss some recent theoretical results concerning the complexity and approximability of this optimization problem, for the basic case where traffic grooming is not allowed (g = 1), and for the general case of traffic grooming (g > 1). BACKGROUNDIn order to utilize the potential of optical fiber, wavelength-division multiplexing (WDM) is used. The bandwidth is partitioned into a number of channels at different wavelengths. Several signals can be transmitted through a fiber link simultaneously on different channels. The number of channels (wavelengths) available in WDM systems is limited by the chosen technology. One of the important parameters affected by the technology is the network cost. Add/drop multiplexers (ADMs) are employed at the network nodes to insert lightwaves into the fiber and extract them. Our goal is assign wavelengths to a given set of lightpaths with a minimum total number of ADMs.[15] is an excellent reference to the basic terms in optical networks.The problem of minimizing the number of ADMs in optical networks design was introduced in [12] (see also [14]), and traffic grooming was introduced in [13]. These studies concentrate on a ring topology for various reasons. One of the commonly stated reasons is that higher level networks which make use of the WDM network cannot necessarily support arbitrary topologies. The most widely deployed network above the WDM layer is the SONET/SDH self-healing rings. These networks have to be configured in rings for protection purposes. An excellent review of the basic traffic grooming problem and many of its variations can be found in [18].These problems are defined as follows: we are given an optical network whose underlying topology is a graph G, and a set of lightpaths which are simple paths in G. We have to assign a color (= wavelength) to each of the lightpaths, so that lightpaths of the same color are edge-disjoint. Each lightpath uses two ADMs, one at each of its endpoints. One ADM can serve lightpaths that arrive from at most two adjacent edges. In other words, two lightpaths of the same color that have a common endpoint can share their ADM at that endpoint. The goal is to find a coloring of the lightpaths that minimizes the total number of ADMs. This problem can be extended by introducing the notion of grooming. When grooming of lightpaths is allowed, up to g lightpaths of the same color can be groomed so that they use the same edge; g ≥ 1 is termed the grooming factor. One ADM can serve lightpaths that arrive from at most two adjacent edges (and therefore one ADM can be used by at most 2g lightpaths). The goal is to find a coloring of the lightpaths that minimi...