Multicasting and Broadcasting in Large WDM Networks

• Venue: IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
• Year: 1998

We address the issue of multicasting and broadcasting in wide area WDM networks in which a source broadcasts a message to all members in S (驴 V). We formalize it as the optimal multicast tree problem which is defined as follows. Given a directed network G = (V, E) with a given source s and a set S of nodes. |V| = n and |E| = m. Associated with every link e 驴 E, there is a set 驴(e) of available wavelengths on it. Assume that every node in S is reachable from s, the problem is io find a multicast tree rooted at s including all nodes in S such that the cost of the tree is the minimum i n terms of the cost of wavelength conversion at nodes and the cost of using wavelengths on links. That is, not only do we need to find such a tree, but also do we need to assign a specific Wavelength 驴 驴 驴(e) to each directed tree edge e and to set the switches at every node in the tree. We show the problem is NP-complete, and hence it is unlikely that there is a polynomial algorithm for it. We further prove that there is no polynomial approximation algorithm which delivers a solution better than (1 - 驴驴) In n times the optimum unless there is an nO(log log n) time algorithm for NP-complete problems, for any fixed 驴驴 with 0 2n + km + kn log(kn) + (kn)1/驴|S|), and delivers a solution within O(|S|驴) the optimum for any fixed 驴 with 0