Wavelength assignment in multifiber star networks

Abstract

We consider the wavelength assignment problem in WDM optical networks with multiple parallel fibers: Given a set P of paths, assign a color to each path such that the number of paths with the same color containing any link is at most the number of fibers in the link. Assuming the number of fibers in each link is fixed, we study two optimization problems. One is to minimize the number of colors for coloring P . The other is to color as many paths of P as possible with a given number of colors. We show that both the minimization and the maximization problems are NP-hard in star networks with a uniform odd number of fibers. We give polynomial time optimal algorithms for the minimization and maximization problems in star networks with an even number of fibers and in the generalized star networks with a uniform even number of fibers. We also give a 1.58-approximation algorithm for the maximization problem in the generalized star networks with an arbitrary number of fibers. The algorithms for the maximization problem in the generalized stars are based on our newly developed algorithm, which optimally solves the call control problem in the generalized star networks. The call control algorithm is of independent interest.

Robust spectrum allocation in elastic flexgrid optical networks: Complexity and formulations

“…Given a predefined routing, the corresponding wavelength assignment and spectrum allocation problems determine the minimum number of wavelengths/slots needed. Since the wavelength assignment problem requires the allocation of a single wavelength to each routing path, the problem is equivalent to a vertex coloring problem in the so‐called conflict graph . The spectrum allocation problem (SA) in flexgrid optical networks is more complex by the contiguous property of the allocated slots and generalizes the vertex coloring problem accordingly.…”