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研究生: 陳明裕
Chen, Ming-Yu
論文名稱: 利用Adleman-Lipton模型求解圖形同構問題
DNA Solution to the Graph Isomorphism using Adleman-Lipton Model with Sticker
指導教授: 謝孫源
Hsieh, Sun-Yuan
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年: 2006
畢業學年度: 94
語文別: 英文
論文頁數: 33
中文關鍵詞: DNA運算DNA演算法分子運算圖形同構問題生物運算
外文關鍵詞: the graph isomorphism problem, DNA-based computing, NP-complete, biological operations, DNA-based algorithms, molecular computing
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  • 自從實驗證明DNA運算的可行性,它已經被廣泛應用在決策與組合性最佳化問題。證明圖形同構問題是否屬於NP問題被認為是棘手的事,儘管可能不是屬於NP-Complete問題。在這篇論文中,我們利用這個運算模型有效率解決圖形同構問題來展示DNA運算的強大。使用stickers產生解法空間以及線性的基本生物運算,我們可以得到DNA演算法來解決這個問題。

    Since the experimental demonstration of its feasibility, DNA-based computing has been applied to a number of decision or combinatorial optimization problems. The graph isomorphism problem belongs to the class of NP problems, and has been conjectured intractable, although probably not NP-complete. In this paper, we demonstrate the power of DNA-based computing by showing the graph isomorphism problem can be efficiently solved under this computation model. By generating the solution space using stickers, we present DNA-based algorithms to solve the problem using polynomial number of basic biological operations.

    1 Introduction 4 2 Models overview 7 2.1 Stickers 7 2.2 The Adleman-Lipton model 8 3 Sticker-based solution space 10 3.1 Generating the permutation set 11 3.2 Adjacency relation representation 16 3.3 Comparing two graphs 22 4 A complete algorithm 25 5 Experimental data 27 6 Discussion and Conclusion 31

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