Introduction to algorithms
Multicast routing for multimedia communication
IEEE/ACM Transactions on Networking (TON)
Worst case performance of some heuristics for Steiner's problem in directed graphs
Information Processing Letters
Distributed computation on graphs: shortest path algorithms
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Lightpath (Wavelength) Routing in Large WDM Networks
ICDCS '98 Proceedings of the The 18th International Conference on Distributed Computing Systems
Multicasting and Broadcasting in Large WDM Networks
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
Approximation Algorithms for Directed Steiner Tree Problems
Approximation Algorithms for Directed Steiner Tree Problems
An algorithm for multicast tree generation in networks with asymmetric links
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 1
Lightpath (wavelength) routing in large WDM networks
IEEE Journal on Selected Areas in Communications
Improved neural heuristics for multicast routing
IEEE Journal on Selected Areas in Communications
Multipoint communication: a survey of protocols, functions, and mechanisms
IEEE Journal on Selected Areas in Communications
Multicast routing with end-to-end delay and delay variation constraints
IEEE Journal on Selected Areas in Communications
ARIES: a rearrangeable inexpensive edge-based on-line Steiner algorithm
IEEE Journal on Selected Areas in Communications
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We address the multicast issue in a wide area WDM network in which a source broadcasts its message to some sites in the network. This problem can be formalized as the following optimal multicast tree problem. Given a directed graph G = (V, E) with a source s and a set S of nodes, assume that every node in S (⊂ V) is reachable from s. Associated with every link e ∈ E, there is a set Λ(e) of available wavelengths on it, |V| = n and |E| = m, find a multicast tree rooted at s including all the nodes in S with minimizing the cost of the tree, in terms of the sum of the cost of wavelength conversion at nodes and the cost of using wavelengths on links in the tree. That is, not only do we need to find a directed tree rooted at s, but also do we need to assign a specific wavelength Λ ∈ Λ(e) to every tree edge e and to set the switches at every node in the tree. Since this problem is NP-complete, it is unlikely that there is a polynomial algorithm to find an exact solution for it. Instead, we first present an approximation algorithm for the problem which runs in time O(k2n + km +kn log(kn) + (kn)1/e|S|), and delivers a solution within O(|S|ε) of the optimal, for any fixed 0 ε ≤ 1. We then present a distributed version of the proposed algorithm. The communication and time complexities of the distributed algorithm are O(km) and O(kn) respectively, and the solution delivered is |S| times of the optimal, where k is the number of wavelengths in the network. Finally, we conduct some experiments to verify the applicability of the proposed algorithms. The experimental results matches our algorithmic claims.