Xavier Muñoz

Traffic Grooming in Unidirectional Wavelength-Division Multiplexed Rings with Grooming Ratio C = 6

SONET/WDM networks using wavelength add-drop multiplexing can be constructed using certain graph decompositions used to form a grooming, consisting of unions of primitive rings. The cost of such a decomposition is the sum, over all graphs in the decomposition, of the number of vertices of nonzero degree in the graph. The existence of such decompositions with minimum cost, when every pair of sites employs no more than

Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

frac{1}{6}

Multiprocessor architectures using multi-hop multi-OPS lightwave networks and distributed control

of the wavelength capacity, is determined with a finite number of possible exceptions. Indeed, when the number N of sites satisfies

The Minimal Manhattan Network Problem in Three Dimensions

N equiv 1 pmod{3}

Online Graph Coloring with Advice and Randomized Adversary

, the determination is complete, and when

A multihop multi-OPS optical interconnection network

N equiv 2 pmod{3}

Induced Broadcasting Algorithms in Iterated Line Digraphs

, the only value left undetermined is N = 17. When

A Study of Network Capacity under Deflection Routing Schemes.

N equiv 0 pmod{3}

Unilaterally connected large digraphs and generalized cycles

, a finite number of values of N remain, the largest being N = 2580. The techniques developed rely heavily on tools from combinatorial design theory.

On the unilateral (Δ, D*)-problem

Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely Add-Drop Multiplexers (ADMs for short). We consider the unidirectional ring topology with a generic grooming factor C , and in this case, in graph-theoretical terms, the traffic grooming problem consists in partitioning the edges of a request graph into subgraphs with at most C edges, while minimizing the total number of vertices of the decomposition. n nWe consider the case when the request graph has bounded degree Δ , and our aim is to design a network (namely, place the ADMs at each node) being able to support any request graph with maximum degree at most Δ . The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and we solve the cases Δ = 2 (for all values of C ) and Δ = 3 (except the case C = 4). We also provide lower and upper bounds for the general case.