Maximizing Profits of Routing in WDM Networks

Let G = (V, E) be a ring (or chain) network representing an optical wavelength division multiplexing (WDM) network with k channels, where each edge e j has an integer capacity c j . A request {si , ti} is a pair of two nodes in G. Given m requests {si , ti}, i = 1, 2, . . . , m, each with a profit value pi , we would like to design/route a k-colorable set of paths for some (may not be all) of the m requests such that each edge e j in G is used at most c j times and the total profit of the set of designed paths is maximized. Here two paths cannot have the same color (channel) if they share some common edge(s). This problem arises in optical communication networks. In this paper, we present a polynomial-time algorithm to solve the problem when G is a chain. When G is a ring, however, the optimization problem is NP-hard (Wan and Liu, 1998), we present a 2-approximation algorithm based on our solution to the chain network. Similarly, some results in a bidirected chain and a bidirected ring are obtained.