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研究生: 高惇信
Tun-Hsin Kao
論文名稱: 加速極大團列舉於類Moon-Moser圖
Accelerating Maximal Clique Enumeration in Moon-Moser-Like Graphs
指導教授: 陳省隆
Hsing-Lung Chen
呂政修
Jenq-Shiou Leu
口試委員: 陳省隆
Hsing-Lung Chen
呂政修
Jenq-Shiou Leu
陳郁堂
Yie-Tarng Chen
莊博任
Po-Jen Chuang
學位類別: 碩士
Master
系所名稱: 電資學院 - 電子工程系
Department of Electronic and Computer Engineering
論文出版年: 2022
畢業學年度: 111
語文別: 中文
論文頁數: 49
中文關鍵詞: 極大團列舉Moon-Moser圖類Moon-Moser圖
外文關鍵詞: Maximal clique enumeration, Moon-Moser graphs, Moon-Moser-like graphs
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團為一圖中的任兩點皆有連接,亦稱為完全圖,若一團不為其它團的子圖時,則稱為極大團。在社群網路蓬勃發展的時代,群體分析變得越來越重要,透過極大團列舉演算法能快速找出關係密切的群體。Bron-Kerbosch演算法經由Tomita與Eppstein等人改良已提升不少效能,但是碰到類Moon-Moser圖時,會讓計算時間變得冗長。我們將透過切割這種稠密圖,尋找各個群組的區域極大團來降低計算時間,最後僅須組合各個群組的區域極大團,就能得到所有的全域極大團。


In a graph, a clique, also called a complete graph, is a subgraph where every two vertices are adjacent. When there is no vertex which can enlarge a clique, it is a maximal clique. The more popular social communities become, the more important network analysis is. By using algorithms of maximal clique enumeration, we can find large communities quickly. Although the Bron-Kerbosch algorithm has been improved by Tomita, Eppstein and others, it fails to deal with Moon-Moser-like graphs efficiently. By dividing this kind of graphs, we can achieve maximal clique enumeration separately to reduce computation time. In the end, we can combine local maximal cliques to get global ones easily.

摘要 IV ABSTRACT V 誌謝 VI 圖表索引 IX 第一章、緒論 1 1.1 研究背景 1 1.2 研究目的 4 1.3 相關應用 5 第二章、相關研究 6 2.1 BK演算法 8 2.2 BKP演算法 11 2.3 BKD演算法 14 2.4 GP演算法 17 第三章、BKG演算法 18 3.1 演算法設計 18 3.2 演算法流程 22 第四章、實驗與分析 27 4.1 實驗環境 27 4.2 測試資料 27 4.3 實驗數據 28 第五章、結論 33 參考文獻 34 附錄 36

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