2001/01/10 by Timothy Y. Chow, Chow, Timothy Y., Philip J. Lin +1
Computer Science · Engineering · Mathematics · #Advanced Optical Network Technologies #Network Traffic and Congestion Control #Software-Defined Networks and 5G #math.CO #math.OC #msc:68W25 #msc:90B10 #msc:94C30
paper · pdf · doi:10.48550/arxiv.math/0101091
Results extended from uniform traffic to quasi-uniform traffic
arxiv created 2003/12/29 · arxiv updated 2009/11/30
The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ``ring grooming problem'' of minimizing the number of add/drop locations instead of the number of rings; in a number of situations this is a better approximation to the true equipment cost. Our main result is a new lower bound for the case of uniform traffic. This allows us to prove that a certain simple algorithm for uniform traffic is in fact a constant-factor approximation algorithm, and it also demonstrates that known lower bounds for the general problem--in particular, the linear programming relaxation--are not within a constant factor of the optimum. We also show that our results for uniform traffic extend readily to the more practically important case of quasi-uniform traffic. Finally, we show that if the number of nodes on the ring is fixed, then ring grooming is solvable in polynomial time; however, whether ring grooming is fixed-parameter tractable is still an open question.