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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.
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