裝置對裝置(Device-to-Device, D2D)技術為一種適用於人群快速交換訊息的解決方案。訊息的交換不需要經過集中式的來源或基地台，而是由各個裝置彼此之間直接完成。在我們的模型中，假設一開始有一個擁有訊息的來源節點，它可以將訊息傳送給它所信任的對象。該來源節點與d個叢集(clusters)相連，而所有叢集中的訊息傳遞方式皆採用D2D技術。每個叢集中的使用者不信任其他叢集的使用者，只信任同一叢集內的成員。也就是說，他們只會與同一叢集內的使用者以及來 源節點互相傳遞訊息。
在本論文中，我們專注於研究在具有來源節點的叢集中的訊息廣播問題，並提供一種效率良好的最佳化排程方式。我們首先考慮這樣的情況:每個叢集中的節點在每一輪中只能將訊息傳送給同一叢集內的另一個節點。當所有叢集中的使用者總數為n而叢集的數量為d時，我們透過貪婪演算法提出一個O(d + log n) 時間複雜度的解法，並證明其為最佳解。接著，我們將進一步討論當每個節點在每輪中可以 將訊息傳送給多個同叢集內節點的情況。我們提出的解法不僅容易實作，亦能在最佳的執行時間內達成最佳排程。

Device-to-Device (D2D) technology is proposed as a solution for a group of people to exchange messages quickly. The exchange of messages does not need to pass through a centralized source or base station, and the devices could finish the work by themselves. In our model, we consider that there is a source which holds a message originally and could send the message to whom it trusts. Apart from the source, all the other nodes are organized in d clusters. Nodes within each cluster are communicated by D2D, so that they only trust the nodes in the same cluster, and do not trust any node from the other clusters. That is, they only send and receive the message from the nodes in the same cluster or the source.
In this thesis, we focus on a special broadcasting problem under this setting. We initially consider the case that the nodes in each cluster send to exactly one node in the same cluster in each round. When n denotes the total number of nodes and d the number of clusters, we propose an O(d + log n)-time greedy method that gives an optimal broadcasting schedule with the minimum number of rounds. Then, we extend the discussion to the case where nodes in each cluster could send to more than one other node in the same cluster in each round. In summary, all the proposed methods are easy to implement, and give an optimal schedule using optimal execution time.