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Wavelength Assignment in Optical Networks with Fixed Fiber Capacity
 

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.

  

Source: Andrews, Matthew - Mathematics of Networks and Systems, Mathematical Sciences Research Center, Bell Laboratories

 

Collections: Mathematics; Computer Technologies and Information Sciences