Efficient Schemes for Parallel Communication
Journal of the ACM (JACM)
Lightwave networks based on de Bruijn graphs
IEEE/ACM Transactions on Networking (TON)
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Wavelength requirements of all-optical networks
IEEE/ACM Transactions on Networking (TON)
Routing and wavelength assignment in all-optical networks
IEEE/ACM Transactions on Networking (TON)
Adaptive wavelength routing in all-optical networks
IEEE/ACM Transactions on Networking (TON)
Permutation routing in wavelength-routed wrapped-around shuffle networks using fewer wavelengths
Computer Networks and ISDN Systems
Improved bounds for all optical routing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Efficient routing and scheduling algorithms for optical networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Design of the optical path layer in multiwavelength cross-connected networks
IEEE Journal on Selected Areas in Communications
IEEE Journal on Selected Areas in Communications
Lightpath (wavelength) routing in large WDM networks
IEEE Journal on Selected Areas in Communications
Edge-disjoint spanning trees for the generalized butterfly networks and their applications
Journal of Parallel and Distributed Computing - Special issue: Design and performance of networks for super-, cluster-, and grid-computing: Part II
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This paper considers randomized routing in wavelength-routed wavelength division multiplexed (WDM) networks. Randomized routing is advantageous when compared to deterministic routing, as it is simple, oblivious, and suitable for centralized as well as distributed implementation. Recently, there has been a considerable interest in studying regular graphs such as shuffle networks and de Bruijn networks as a possible physical topology for wavelength-routed WDM networks (IEEE/ACM Trans. Network 3(3) (June 1995) 269; IEEE/ACM Trans. Network 2(1) (February 1994) 70; Comput. Networks ISDN Systems 30(24) (December 1998) 2349). In Pankaj and Gallager (1995), permutation routing has been taken as a benchmark problem to accept a network and a deterministic algorithm has been proposed for routing permutation traffic without any blocking in an N-node wrapped-around multi-stage shuffle network using O(log3 N) wavelengths.In this paper, we look at the possible application of probabilistic techniques on a class of wrapped-around multi-stage networks called 2-multinets and study the wavelength requirements for routing permutation traffic, allowing a negligible blocking of sessions. We adopt the routing scheme proposed in (J. ACM 31 (1984) 507) for fast packet routing to find routes in the circuit-switched wavelength-routed WDM networks and analyze the wavelength requirements for different models. The models differ in their routing node architecture and wavelength selection policy. Our analysis shows that the permutation routing problem can be solved on these models with an overwhelming probability using O(log2 N) wavelengths. We also study the routing problem on 2-multinets for a class of 1-expectedly bounded connection requests. For this class also, we propose two models and obtain similar bounds on the number of wavelengths required. We confirm the theoretical results by extensive simulation experiments. The theoretical as well as experimental results show that the number of wavelengths required is reduced significantly when randomized routing techniques are used. Finally, we discuss how the results obtained for 2-multinets can be extended to hypercubes and de Bruijn networks.