點對點(Peer-to-Peer)網路系統可區分為結構化(Structured)與非結構化(Unstructured)架構，其特點在於突破傳統的主從式(Client/Server)網路系統結構，本研究主要針對非結構化網路系統之搜尋方式進行探討與改良，從而發展出一套更有效率的搜尋演算法。在非結構化點對點網路系統中，傳統的資源搜尋機制為洪水搜尋演算法(Flooding)，該方法是將每個節點(Node)所發出或接收到的查詢訊息(Query Message)轉送給所有跟自己相連接的節點，直到TTL(Time-to-Live)的值等於零為止。然而，在這個無任何查詢策略的盲目搜尋演算法中，在大規模點對點網路系統裏將造成大量的頻寬浪費。在本研究中，藉著我們設計的統計式矩陣計算機制(Statistical Matrix Form, SMF)去辨別鄰近節點的相關能力，包括資源查詢、服務轉發、分享及暫存功能以及搜尋路徑挑選等隱含統計資訊計算，從中挑選出能力較強的節點來傳送及轉發查詢訊息，進而改善其搜尋效能。在廣大的網路系統中，每個節點在不同性質包括分享數量、分享品質、服務意願以及傳輸時間等方面皆各有差異。因此針對此觀點，我們將這些性質導入我們提出的數學統計資訊運算架構裡，進而演化成SMF；透過此搜尋機制，我們將可以大量的改善搜尋效能。無論在理論以及實驗的分析方面，皆証明出我們所提出的方法是有效且實用的。

Flooding is a traditional file search mechanism in unstructured Peer-to-Peer (P2P) systems in which a peer broadcasts a query to its neighbors until the time-to-live (TTL) decreases to zero. However, this blind choice strategy usually creates enormous traffic costs within a large network. In this paper, we seek to improve search performance in un- structured P2P networks by choosing neighbors' abilities through power-theoretic pattern we named Statistical Matrix Form (SMF). In networks, peers are different from each other in many aspects, such as sharing numbers, content quality, query service and transport efficiency between neighbors. We designed SMF to measure these features in our math- ematic model to compute neighbors' abilities so higher capabilities can be determined in order to significantly reduce traffic costs. Both theoretical and experimental analyzes have been demonstrated to be effective and efficient in our proposed method.

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