Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture
SIAM Journal on Computing
IEEE/ACM Transactions on Networking (TON)
Cost-effective traffic grooming in WDM rings
IEEE/ACM Transactions on Networking (TON)
On optimal traffic grooming in WDM rings
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
A 10/7 + " Approximation for Minimizing the Number of ADMs in SONET Rings
BROADNETS '04 Proceedings of the First International Conference on Broadband Networks
Design Theory
Better bounds for minimizing SONET ADMs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Traffic grooming in WDM networks
IEEE Communications Magazine
Grooming of arbitrary traffic in SONET/WDM BLSRs
IEEE Journal on Selected Areas in Communications
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
Theoretical Computer Science
A 10/7 + ε approximation for minimizing the number of ADMs in SONET rings
IEEE/ACM Transactions on Networking (TON)
Approximating the traffic grooming problem in tree and star networks
Journal of Parallel and Distributed Computing
Approximating the traffic grooming problem
Journal of Discrete Algorithms
Approximating the Traffic Grooming Problem with Respect to ADMs and OADMs
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
On the complexity of the traffic grooming problem in optical networks
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
Approximating the traffic grooming problem in tree and star networks
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Approximating the traffic grooming problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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In a WDM network, routing a request consists in assigning it a route in the physical network and a wavelength. If each request uses at most 1/C of the bandwidth of the wavelength, we will say that the grooming factor is C. That means that on a given edge of the network we can groom (group) at most C requests on the same wavelength. With this constraint the objective can be either to minimize the number of wavelengths (related to the transmission cost) or minimize the number of Add Drop Multiplexer (shortly ADM) used in the network (related to the cost of the nodes). Here we consider the case where the network is a path on N nodes, PN. Thus the routing is unique. For a given grooming factor C minimizing the number of wavelengths is an easy problem, well known and related to the load problem. But minimizing the number of ADM's is NP-complete for a general set of requests and no results are known. Here we show how to model the problem as a graph partition problem and using tools of design theory we completely solve the case where C = 2 and where we have a static uniform all-to-all traffic (requests being all pairs of vertices).