隨著網際網路的快速發展，如何有效率地在網路上傳輸檔案已成為一項重要議題。
其中一個相關問題為「廣播問題（broadcasting problem）」，最早由Farley 於1980 年
研究[5]。此問題引發了諸多延伸議題的研究，而我們特別關注Lin 於2018 年提出的
最少回數優先傳播問題（Prioritized Optimal Round File Dissemination Scheduling, 簡
稱PORFDS）[9]。PORFDS 是一個在無向圖網路中，從來源節點將檔案廣播至整個網
路的問題。為了降低網路壅塞，該問題額外加入了一項新限制：最大負載最小化。
Lin [9] 與Chen [2] 針對此問題提出了解法。在本論文中，我們特別針對PORFDS
的最後一輪傳輸進行研究，因為該輪為目前解法的瓶頸。我們考慮兩種輸入網路拓
樸：路徑拓樸（path topologies）與樹狀拓樸（tree topologies）。針對路徑輸入，我們
提出一個線性時間複雜度的貪婪演算法，相較之下， Chen 所提出的演算法時間複雜
度為O(n log r)，其中r 代表網路中接收節點的數量。針對樹狀輸入，我們設計了一
個O(n log r) 時間的演算法，其靈感來自Chen 所提出的O(n2 log r) 演算法啟發，但採
用了不同且更高效的方法。
關鍵字: 檔案傳播、網路壅塞、最大負載最小化、路徑拓樸、樹狀拓樸

With the rapid development of the Internet, the efficiency of file transfer has become
a significant issue. One such problem is the broadcasting problem, first studied by Farley
[5] in 1980. Various related problems have been discussed, and we are especially
interested in the Prioritized Optimal Round File Dissemination Scheduling (PORFDS)
problem introduced by Lin [9] in 2018. PORFDS is a broadcasting problem on an undirected
graph network that disseminates a file from a source node to the entire network in
rounds. To reduce network congestion, an additional constraint—minimizing the maximum
busload—is added. Lin [9] and Chen [2] proposed algorithms for this problem. In
this thesis, we focus on the final transmission round of PORFDS since it is the bottleneck
of existing algorithms. We consider two types of input networks: path topologies and
tree topologies. For path inputs, we design a greedy algorithm that improves the time
complexity from Chen’s O(n log r) to O(n), where r denotes the number of receiver nodes
in the network. For tree inputs, we give an O(n log r)-time algorithm, which is inspired
by Chen’s O(n2 log r) algorithm [2] but with a different and more efficient approach.
Keywords: File dissemination, network congestion, minimizing maximum busload, path
topology, tree topology