核心基礎轉發群播樹 (Core-based Forwarding Multicast Tree) 是一種以核心節點 (Core Node) 為樹根的最短路徑樹。網路中任何欲群播至特定群組的封包會被送至核心節點，並由核心節點透過群播樹將封包發送給群組中的所有成員。傳統上想要降低網路頻寬的花費，是透過建立一個擁有最低總邊權重 (Minimum Total Weights of Edges) 和並能擴張 (Span) 所有群組成員的群播樹。然而，當區域性廣播 (Local Broadcast) 的特性被利用來群播一個封包時，頻寬花費應該改變為評估所有傳送者 (核心節點以及所有的非葉節點) 的權重和。當群播樹節點的個數為三個以上並且只有在核心節點不為葉節點時會擁有最低的頻寬花費，這個特性引導我們在一個所有傳送節點皆設定為一單位權重的網路中，尋找擁有最少非葉節點的群播樹。然而，除非在 P 等於 NP的情況下，否則最少非葉節點群播樹問題 (Minimum Non-Leaf Multicast Tree Problem) 並沒有多項式時間逼近方法 (Polynomial Time Approximation Scheme) 。因此我們發現這個問題不僅是一個 NP-hard 問題，也是一個 MAX-SNP hard 問題，於是我們提出了一個動態減少群播樹中非葉節點的方法。實驗結果顯示群播樹結合了我們的方法之後，擁有比起其他方法還要少的非葉節點數目。

A core-based forwarding multicast tree is the shortest path tree rooted at a core node that distributes multicast packets to all group members via the tree after the packets are sent to the core. Traditionally, the bandwidth cost is minimized by constructing the multicast tree that has minimum total weights of edges to span all group members. However, when the local broadcast operation is used to multicast a packet, the bandwidth cost is supposed to be evaluated by the total weights of all senders that include the core and all non-leaves. Since the multicast tree with at least three nodes has minimum bandwidth cost only when the core is not a leaf, it leads us to find the multicast tree with the minimum number of non-leaves when each sender node has a unit weight. However, no polynomial time approximation scheme can be found for the minimum non-leaf multicast tree problem unless P=NP since the problem is not only NP-hard but also MAX-SNP hard. Thus, a distributed algorithm is proposed to dynamically reduce the number of non-leaves in the multicast tree. Experimental results show that after the execution of our method, the multicast tree has a lesser number of non-leaves than others.

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