當我們對一個圖形動態的增減線段，並對改變後的圖形作一些圖形性質的詢問 - 如 ”連結性”、”最小展開樹”、”平面性” 等 – 此類的問題我們稱作 “動態圖形問題”。 其中，”在圖形G中，點v和點w是連結的嗎? ” 或 “圖形G是連結的嗎?” 這類問題是屬於 “動態連結問題”。此類問題若能容許線段增加和減少，我們稱之為”全動態”。若只容許線段增加，我們稱為 ”遞增式”。同樣的，若只容許線段減少，就稱之為”遞減式”。 有效率的動態圖形演算法已發現在 “通訊網路”，”CAD”，”資料庫系統”，”邏輯程式設計”，”遞增式資料流量分析”，甚至”計算生物學”都有應用。而全動態以及遞增式圖形問題已有許多人做了廣泛的研究，也得到不錯的結果。在此篇碩士論文中，焦點放在遞減式的連結問題。提供了一個演算法，需要O(n) 的前置處理時間及空間，和O(log n / log log n) 的詢問時間及資料結構更新時間。

A dynamic graph problem is to maintain a graph G=(V, E), where G may be updated by insertion and deletion of edges and queries concerning certain properties of G may be asked. For the dynamic connectivity problem, the queries are of the form: “Are vertices v and w connected in G ?” or “Is G connected?” A dynamic graph problem is fully dynamic if both insertions and deletions of edges are allowed. The problem is incremental if only insertions are allowed, and decremental if only deletions are allowed. Efficient dynamic graph algorithms have many applications in communication networks, computer-aided design, database systems, logic programming, incremental data flow analysis, and computational biology.
In this thesis, the decremental dynamic connectivity problem in outerplanar graphs is studied. An efficient algorithm is presented. The presented algorithm requires O(n) space. After an O(n) time preprocessing, each edge deletion and connectivity query can be done in O(log n / log log n) time.

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