本篇論文主要在探討 directed Steiner tree problem(DSTP)的近似演算法。Directed Steiner Tree問題為：給定一有向加權圖G=(V,E,c)，V為節點集合，E為邊的集合，對於G中的任一條邊上都存在一個實數c，稱c為此邊的成本。此外，V集合中存在一個節點r以及一個子集合X，稱此節點r為root，X集合為terminal 集合。目標為在G中找到一棵以r為根，衍生至X集合中所有節點的最小成本樹，也就是說，此最小成本樹包含r至X集合中所有節點路徑。在此之前，Charikar et al.等人提出了一個以遞迴方式建構Steiner的DSTP演算法，但是在這樣的遞迴演算法中，當遞迴層數越高時，時間複雜度成指數成長，相當可觀，且在演算法中有過多重複的遞迴呼叫。因此，本篇論文基Charikar’s algorithm，改進其演算法中過多重複運算的情況，提出modified　Charikar’s algorithm with improvement on terminal(MCAIT)以及modified Charikar’s algorithm with improvement on　terminal and　vertex(MCAITV)。接著，本篇論文亦提出group　terminal 的概念，將此概念導入MCAIT 及MCAITV 中，提出group algorithm with improvement on terminal(GAIT)以及group algorithm with improvement on terminal and vertex(GAITV)。
　　本篇論文中亦證明四個演算法的approximation bound和Charikar's algorithm相同，但時間複雜度皆較Charikar's algorithm的時間複雜度低並且在模擬的結果可以得知我們的方法相較於Charikar’s　algorithm 在運行速度上有顯卓的改善。

第一章 簡介 1
第二章 相關演算法回顧 3
第三章 MCAIT 18
第四章 MCAITV 58
第五章 Group Algorithm 83
第六章 模擬與結果 115
第七章 結論 126
第八章 參考文獻 127

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