隨著全球互聯網的日益普及，點對點文件共享已成為其最重要的應用程式
之一，因為它允許在同儕之間相互協作，有效地廣播文件。相關的正式研究可
以追溯到Farley (1980)，其重點是尋求在最少的回數內完成整個廣播過程。在
某些點對點文件共享的使用中，同儕可能存在不同的優先等級，其中具有較高
優先等級的同儕應該更早接收文件。Lin (2009) 提出了「最少回數優先資料傳
播」(PORFDS) 問題，其中重點是設計使用最少回數的同時, 亦加入了優先等級
的考量；而當有多個資料傳播方式可用時，我們將選擇一個讓最大「負載」的
邊其使用量為最小的方式。
Lin (2009) 發現，當通訊網路是由n 個節點組成的路徑時，且節點的優先權
符合「重覆倍增」的條件，則若n為2的冪次方時，這樣的問題可以在O(n) 時
間內解；而若n不是2的冪次方時，則時間為O(n log2 n)。在本論文中，我們將
後者的時間改進為O(n)。此外，我們擴展了Lin (2009) 的研究，新增了對另外
兩種類型網絡–樹和有向循環–的探討，並提出了解決這些情況下PORFDS 問題
的有效演算法。

Amid the surging popularity on worldwide internet, peer-to-peer file sharing
has become one of the most important applications, as it allows for efficient broadcasting
of a file among the peers collaboratively. A formal study can be dated as
early as Farley (1980) whose focus is on finishing the broadcasting process in the
minimum number of rounds.
In some peer-to-peer applications, there may be different levels of priority,
where peers with a higher priority should receive the file earlier. Lin (2009) proposed
the prioritized optimal-round file dissemination schedule (PORFDS) problem,
where the focus is to design broadcasting scheme that uses minimum rounds
for the whole process, while taking priority into consideration; further, when more
than one schedule is available, we will choose one such that the maximum load, or
usage, among all edges for communication, is minimized.
Lin (2009) showed that when the communication network is an n-node path,
and the priority of the nodes obey the doubling condition, such a problem can be
solved in O(n) time when n is a 2-power, and O(n log2 n) time when n is not a
2-power. In this thesis, we improve the latter result to O(n) time. Moreover, we
extend Lin’s study for two other types of network, namely tree and directed cycle,
and propose efficient algorithms for solving the corresponding PORFDS problems

[1] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
Introduction to Algorithms (3rd Edition). MIT Press, 2009.
[2] Arthur M. Farley. Broadcast Time in Communication Networks. SIAM Journal
on Applied Mathematics, 39(2):385–390, 1980.
[3] Yi-Hsun Lin. Minimize the Maximum Busload under the Prioritized Optimal-
Round File Dissemination Schedule. Master’s thesis, National Tsing Hua University,
Taiwan, 2009.
[4] Mario Eduardo Rivero- ´Angeles and Gerardo Rubino. Priority-Based Scheme
for File Distribution in Peer-to-Peer Networks. In Proceedings of IEEE International
Conference on Communications, pages 1–6, 2010.