本篇論文主要在探討directed Stenier tree problem(DSTP)的近似演算法，基於Charikar及T.W.Chang的演算法，加入了sparse splitting nodes的觀念，給予節點分枝限制，推導出此種狀況下l-restricted tree的bound並設計出針對以上五種演算法的sparse splitting nodes對應版本。

It researchs for approximation algorithms of directed steiner tree problem and add an idea of sparse splitting nodes.

摘要................................................................................................................................ I
目錄............................................................................................................................... II
圖目錄..........................................................................................................................IV
表格目錄......................................................................................................................VI
第一章 簡介............................................................................................................1
第二章 相關演算法................................................................................................3
2.1. Basic Definition .........................................................................................3
2.2. l-restricted tree ...........................................................................................4
2.3. Charikar’s algorithm..................................................................................5
2.4. MCAIT.......................................................................................................8
Charikar’s algorithm問題分析.....................................................8
過多的重複運算之改進概念.......9
MCAITV..................................................................................................10
Charikar’s algorithm問題分析...................................................10
()11,,iAvkX−至()1,,inAvkX−中過多的重複運算之改進概念.11
2.6. Group algorithm.......................................................................................11
第三章 Directed Steiner Tree with Sparse Splitting Nodes Problem...................13
3.1. Sparse Splitting Nodes 問題分析...........................................................13
3.2. l-restricted tree .........................................................................................13
l-restricted tree algorithm with sparse splitting nodes .................13
l-restricted tree algorithm with sparse splitting nodes .................16
3.3. CASSN.....................................................................................................24 II
3.4. CAITSSN.................................................................................................33
3.5. CAITVSSN..............................................................................................42
3.6. GAITSSN.................................................................................................52
3.7. GAITVSSN..............................................................................................60
3.8. 時間複雜度..............................................................................................68
Charikar’s algorithm時間複雜度分析.......................................68
各演算法時間複雜度比較..........................................................69
第四章 模擬與結果..............................................................................................70
4.1. 環境設定..................................................................................................70
4.2. 模擬結果與分析......................................................................................71
Edge成本為1~10的實數..........................................................71
Edge成本為1 .............................................................................76
第五章 結論..........................................................................................................81
第六章 參考文獻..................................................................................................82

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