We present a heuristic for solving the discrete maximum-minimum (maxmin) rates for dense WDM- (DWDM-) based optical subnetworks. Discrete maxmin allocation is proposed here as the preferred way of assigning wavelengths to the flows found to be suitable for lightpath switching. The discrete maxmin optimality condition is shown to be a unifying principle underlying both the continuous maxmin and discrete maxmin optimality conditions. Among the many discrete maxmin solutions for each assignment problem, lexicographic optimal solutions can be argued to be the best in the true sense of maxmin. However, the problem of finding lexicographic optimal solutions is known to be NP-complete (NP is the class that a nondeterministic Turing machine accepts in polynomial time). The heuristic proposed here is tested against all possible networks such that |Γ + Ω| ≤ 10, where Γ and Ω are the set of links and the set of flows of the network, respectively. From 1,084,112 possible networks, the heuristic produces the exact lexicographic solutions with 99.8% probability. Furthermore, for 0.2% cases in which the solutions are nonoptimal, 99.8% of these solutions are within the minimal possible distance from the true lexicographic optimal solutions.
© 2002 Optical Society of AmericaPDF Article