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 Title: 穩定婚姻及穩定配偶的模擬;The Simulation of Stable Marriage and Stable Pairs Authors: 顏志瑜;Chih-yu Yen Contributors: 數學研究所 Keywords: 穩定婚姻;穩定配偶;stable marriage;stable pairs Date: 2010-07-21 Issue Date: 2010-12-08 14:26:26 (UTC+8) Publisher: 國立中央大學 Abstract: 本文主要在於探討穩定配對中的穩定婚姻問題，提及穩定男伴、拆散配對以及P循環的概念，重新推導 Knuth, Motwani 與 Pittel 的結論: 對任何女生的穩定男伴為至少 max(0,(1/2-epsilon)lnn ，最多為 (1+epsilon)lnn 個的機率趨近 1，當n → ∞ 時，其中 0< varepsilon <1 。並介紹兩種方法找到所有的穩定配對，透過 C++ 模擬結果比較各方法的優缺點，並與理論值作比對。 In this paper we study the stable marriage and stable husbands problems of stable matching, using the concept of breakmarriage and p-cycle, and revisit the result of Knuth ,Motwani and, Pittel : any particular girl has at least max(0, (1/2−epsilon) ln n) and at most (1+epsilon) ln n different husbands, with probability approaching 1 as n → ∞, if 0 < epsilin < 1. We introduce two methods to find all stable matchings and simulate in C++ programming language to compare these two methods and theoretical results. Appears in Collections: [數學研究所] 博碩士論文

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