自從網際網路的蓬勃發展，各式各樣的網路應用如雨後春筍般出 現。大量信息在網路間傳播的方法不久就成為許多研究者研究的重 要議題。然而，大量信息傳播時資訊的信賴與安全問題也很快地被 大家重視，有些人研究了關於信賴模型底下使用最少回數的資料傳 播模型，這個傳播模型是建立在層次結構底下。層次結構，就是系 統內的點有不同的等級高低，等級低的點只會相信高等級的點傳來 的資訊。在另一方面，我們知道傳播資訊的系統總線觀念從很早就 被應用在電腦中以降低成本。因此在此篇論文中，我們以點的傳播 優先順序代表點之間的信賴關係，結合信賴關係底下最小回數傳播 與最小化系統最大總線的觀念，討論了四種情況底下，在優先順序 模型底下使用最少回數傳播，而能最小化系統總線中最大流量方法。 這四種情況分別為 (1) 預先排定點的優先順序底下，總點數為二的次 方倍 (2) 預先排定點的優先順序底下，總點數非二的次方倍 (3) 未事 先排定點的優先順序底下，總點數為二的次方倍 (4) 未事先排定優先 順序底下，總點數非二的次方倍。

Since the development of Internet, all kinds of network applications have emerged. One of them is the dissemination of a large number of files with efficiency, which has been studied by many researchers. However, apart from efficiency, security and trust have also become a crucial issue concerned by the public, where some have studied the dissemination problem with trust model using minimal rounds with transmission structure organized with hierarchy. By means of hierarchy, some nodes in the network have higher level while others have lower level, and a node will only trust and receive files from nodes with higher level. On the other hand, the concept of shared bus has already been used in computer industry to minimize the system cost in the early years of computer development. In this thesis, we consider nodes having different priorities, and use the priority relationship to define the trust relationship among nodes. We study and show how to minimize the maximum busload of a prioritized file dissemination schedules using optimal rounds on a shared bus. Four different cases are discussed: (i) when the node priorities are predefined and the total number of nodes is a power of 2; (ii) when the node priorities are predefined and the total number of nodes is not a power of 2; (iii) when the node priorities are not predefined and the total number of nodes is a power of 2; (iv) when the node priorities are not predefined and the total number of nodes is not a power of 2.

摘要 ............................................................................................................................. i
Abstract ...................................................................................................................... ii
1 Introduction .............................................................................................................. 1
1.1 Contribution and Organization ............................................................................. 2
2 Problem Definition ...................................................................................................3
2.1 What is PORFDS? ................................................................................................. 3
2.1.1 Adding Priority Constraint to an FDS ................................................................ 3
2.1.2 Adding Optimal-Round Constraint to FDS ....................................................... 5
2.1.3 Combining Priority and Optimal-Round Constraints ....................................... 7
2.2 Our Problem: Finding a PORFDS that Minimizes the Maximum Busload ......... 7
2.3 Some Terminology .............................................................................................. 9
3 Types of Input .........................................................................................................10
3.1 Predefined Inputs ................................................................................................ 10
3.2 Free Inputs .......................................................................................................... 11
4 Minimizing the Maximum Busload of PORFDS with Predefined Inputs ............. 12
4.1 When the Node Number is a Two Power ........................................................... 12
4.2 When the Node Number is Not a Two Power ................................................... 16
4.2.1 Improving the Time Complexity to O(n log2 n) ............................................... 18
5 Minimize the Maximum Busload of PORFDS with Free Inputs ........................... 19
5.1 When the Node Number is a Two Power ........................................................... 19
5.2 When the Node Number is Not a Two Power ................................................... 22
5.2.1 Using a Rooted Tree to Describe a Schedule ................................................. 23
5.2.2 Limiting the Search Space .............................................................................. 24
5.2.3 Block Expression and Block Expansion .......................................................... 27
5.2.4 The Grammar-Based Block Expansion ........................................................... 28
5.2.5 Finding the Best Grammar-Based Block Expansion ....................................... 31
6 Conclusion and Future Work ................................................................................. 34
References ................................................................................................................ 35

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