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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65623
Title: | 圖的均勻邊切割問題 Uniform Edge-Partition of a Graph |
Authors: | An-Chiang Chu 朱安強 |
Advisor: | 趙坤茂(Kun-Mao Chao) |
Keyword: | 邊切割,點切割,圖切割,樹,演算法,圖論, edge-partition,vertex-partition,graph partition,tree,algorithm,graph theory, |
Publication Year : | 2012 |
Degree: | 博士 |
Abstract: | 當給定正整數 k 以及對於一個邊數為 n 的無向連通圖,我們關心的是把此圖的邊分割成 k 個連通子圖,使得每一部份的大小盡可能地均勻。在此篇論文以最大塊與最小塊的邊數比來當作衡量的標準。在此課題上,過去的文獻只探討當圖限制為樹的結構,且邊為無權重之情況。對於 k=2,3 及 4 的情況,已被證明最大塊與最小塊的邊數比可以保證在 2 以內。而對於任意的 k ,先前最佳的結果是保證最大塊與最小塊的邊數比在 3 以內。
此篇論文將圖推廣至一個邊有權重的任意連通圖。當每個邊的權重不超過平均權重的一半時,我們提出一個線性時間的演算法來得到此圖的邊切割,使得最大塊與最小塊的邊數比可以保持在 2 以內。此外,我們也藉由一個例證來說明邊權重的限制是最寬鬆的。 Given a positive integer k and an undirected edge-weighted connected simple graph G with n edges, where k ≤ n, we wish to partition the graph into k edge-disjoint connected components of approximately the same size. We focus on the max-min ratio of the partition, which is the weight of the maximum component divided by that of the minimum component. For k = 2,3, and 4, it has been shown that the upper bound of the max-min ratio of an unweighted tree is two. For any k, the best previous upper bound of the max-min ratio of an unweighted tree is three. In this thesis, for any graph with no edge of weight larger than one half of the average weight of a component, we provide a linear-time algorithm for delivering a partition with max-min ratio at most two. Together with the fact that the max-min ratio is at least two for some instances, we have that the max-min ratio upper bound attained in this thesis is tight. Furthermore, by an extreme example, we show that the above restriction on edge-weights is the loosest possible. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65623 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 資訊工程學系 |
Files in This Item:
File | Size | Format | |
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ntu-101-1.pdf Restricted Access | 632.46 kB | Adobe PDF |
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