The SONET edge-partition problem

The edge-partitioning problem presented in this paper is motivated by a problem in the design of SONET telecommunication networks. In a SONET ring, customer sites are connected via a ring of fiber-optic cable, each one sending, receiving, and relaying messages through a device called an add–drop-multiplexer (ADM). A bandwidth request, or demand, is given for every pair of sites. Each SONET ring serves a collection of demand pairs. The capacity of a ring must accommodate the sum of the bandwidth requests of all the demand pairs it serves. The problem is to partition all customer demand pairs into subsets so that the traffic in each subset is bounded by a given capacity limit. A site may be assigned to more than one ring, but the traffic between two sites cannot be split between rings. It is assumed that there are no digital cross connects (DCS) to transfer the traffic from one ring to another. A site requires an ADM for each ring to which it is assigned. The objective is to minimize the total number of the ADMs. The problem can be formulated as an optimization problem defined on an edge-weighted graph. The vertices of the graph correspond to customer sites while the weight of an edge between two vertices corresponds to the bandwidth request for the pair of sites linked by the edge. The problem is then to cover the edges of the graph with a set of edge-disjoint subgraphs such that the total weight of the edges covered by each subgraph is at most a given ring capacity. Since the subgraphs have no edges in common, we say that they partition the edges of the graph. The ring capacity is fixed and determined by the size of the ADMs being used. ADMs come in an industry-standard set of sizes, for example, 155 or 622 megabits per second, and all rings must use the same size ADM. The objective is to minimize the total number of vertices used in all subgraphs, which corresponds to the total number of ADMs. Correspondence to: E. V. Olinick; e-mail: [email protected] Contract grant sponsor: Office of Naval Research; contract grant number: N00014-96-1-0315 Dorit Hochbaum’s research was supported in part by NSF award Nos DMI-0085690, DMI-0084857 and by UC-smart award.