 
Summary: Wavelength Assignment in Optical Networks
with Fixed Fiber Capacity
Matthew Andrews and Lisa Zhang
Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974
{andrews,ylz}@research.belllabs.com
Abstract. We consider the problem of assigning wavelengths to de
mands in an optical network of m links. We assume that the route of
each demand is fixed and the number of wavelengths available on a fiber
is some parameter µ. Our aim is to minimize the maximum ratio be
tween the number of fibers deployed on a link e and the number of fibers
required on the same link e when wavelength assignment is allowed to
be fractional.
Our main results are negative ones. We show that there is no constant
factor approximation algorithm unless NP#ZPP. No such negative re
sult is known if the routes are not fixed. In addition, unless all lan
guages in NP have randomized algorithms with expected running time
O(n polylog(n) ), we show that there is no log # µ approximation for any
# # (0, 1) and no log # m approximation for any # # (0, 0.5). Our anal
ysis is based on hardness results for the problem of approximating the
chromatic number in a graph.
