Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture
SIAM Journal on Computing
A 10/7 + " Approximation for Minimizing the Number of ADMs in SONET Rings
BROADNETS '04 Proceedings of the First International Conference on Broadband Networks
Approximating the traffic grooming problem in tree and star networks
Journal of Parallel and Distributed Computing
On the complexity of the traffic grooming problem in optical networks
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
Hardness and approximation of traffic grooming
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Approximating the traffic grooming problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Minimizing total busy time in parallel scheduling with application to optical networks
Theoretical Computer Science
Optimizing regenerator cost in traffic grooming
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Optimizing regenerator cost in traffic grooming
Theoretical Computer Science
On the complexity of the regenerator cost problem in general networks with traffic grooming
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Online optimization of busy time on parallel machines
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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We consider the problem of switching cost in optical networks, where messages are sent along lightpaths. Given lightpaths, we have to assign them colors, so that at most glightpaths of the same color can share any edge (gis the grooming factor). The switching of the lightpaths is performed by electronic ADMs (Add-Drop-Multiplexers) at their endpoints and optical ADMs (OADMs) at their intermediate nodes. The saving in the switching components becomes possible when lightpaths of the same color can use the same switches. Whereas previous studies concentrated on the number of ADMs, we consider the cost function - incurred also by the number of OADMs - of f(茂戮驴) = 茂戮驴|OADMs| + (1 茂戮驴 茂戮驴)|ADMs|, where 0 ≤ 茂戮驴≤ 1. We concentrate on chain networks, but our technique can be directly extended to ring networks. We show that finding a coloring which will minimize this cost function is NP-complete, even when the network is a chain and the grooming factor is g= 2, for any value of 茂戮驴. We then present a general technique that, given an r-approximation algorithm working on particular instances of our problem, i.e. instances in which all requests share a common edge of the chain, builds a new algorithm for general instances having approximation ratio r茂戮驴logn茂戮驴. This technique is used in order to obtain two polynomial time approximation algorithms for our problem: the first one minimizes the number of OADMs (the case of 茂戮驴= 1), and its approximation ratio is 2 茂戮驴logn茂戮驴; the second one minimizes the combined cost f(茂戮驴) for 0 ≤ 茂戮驴