On DRC-cycle covering in optical networks

Abstract

This paper consider the case when the physical graph G = C tn (a ring of size tn) and logical graph is λK t (n). We want to minimize the number of cycles ρ(n t , λ) in the DRC covering. For this problem, we obtain the optimal solutions when both n and t are odd. 42 Z. Liang and C. Xie / On DRC-cycle covering in optical networksgenerality; in first approximation, we can reduce it to minimize the number of cycles of the covering. We will restrict ourselves to a particular case of the general problem which is interesting for practical networks and shows already the difficulty of the problem. Mainly, we will suppose that the physical network is a ring and the set of requests is the All-to-All one.Compared to previous studies based on a similar approach (see [4,12]), we provide an analytical model and optimal solutions for the ring physical topology. A similar problem was considered in [3] and [5]. They use the same ring survivability conditions but their aim is to minimize the sum of the number of nodes of the rings.Routing problems are found both in the virtual graph and in the physical one. Here we consider a covering problem that the communication requests are routed on sub-networks which are protected independently from each other. We model the WDM network by a graph (called the physical graph), its nodes represent the optical switches and the edges the fiber-optics links. We will consider that the physical graph is either an undirected cycle of length tn, denoted by C tn , or the symmetric directed cycle C * tn . Routing a request over physical graph G consists in finding a path over G between the pair of nodes communicating in the request. We can model all the requests as the edge set of a logical graph I undirected or not. The nodes represent the nodes of the physical graph and the edges correspond to the requests between these nodes. One constraint that each cycle formed by some requests must be routed node disjoint over the physical graph G. We call this property the disjoint routing constraint (DRC).Problem 1.1. Find a cycle decomposition or a cycle covering satisfying DRC property of the edges of I with an associated routing over G such that the number of cycles is minimized. Z. Liang and C. Xie / On DRC-cycle covering in optical networksthe number of cycles t 2 − t