Proposal of new steiner tree algorithm applied to P2MP traffic engineering

There are many polynomial-time heuristic Steiner tree algorithms since seeking the minimum point to multi point (P2MP) tree in a network, which is known as the Steiner problem in networks (SPN), is nondeterministic polynomial time complete. Takahashi and Matsuyama´s minimum-cost path heuristic algorithm (MPH) is widely applied to various multicast services. MPH has to run Dijkstra´s algorithm m times in its algorithm process, where m is the number of end nodes of the multicast tree. By using Fibonacci heaps (F-heaps), the time complexity of MPH is O(m(l + n log n)), where l is the number of links and n is the number of nodes on the network. A new Steiner tree algorithm called branch-based multi-cast (BBMC) is proposed for this study, which produces exactly the same P2MP tree as MPH does. BBMC shortens MPH´s average time complexity to O((log m)(l + n log n)). In addition, the algorithm speed of BBMC is much faster than that of MPH because BBMC does not use Dijkstra´s algorithm in its algorithm process and drastically reduces the number of accesses to the F-heaps. MPH´s processing time increases proportionally to m, especially when m is large, but BBMC´s processing time is almost independent from m. The speed of BBMC is about the same as that of the destination-driven multi-cast algorithm (DDMC), which has a time complexity of O(l + n log n), though BBMC produces a P2MP tree with a tree cost much smaller than that of DDMC.