Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes
碩士 === 朝陽科技大學 === 資訊工程系碩士班 === 100 === The n-dimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional augmented cube AQn, an important variation of the hypercube, possesses several embedding propert...
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ndltd-TW-100CYUT53920162015-10-13T21:17:23Z http://ndltd.ncl.edu.tw/handle/10688943365551438099 Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes 增廣立方體上的二條邊互斥漢彌爾頓迴路及等距路徑覆蓋 Chun-Kai Wang 王俊凱 碩士 朝陽科技大學 資訊工程系碩士班 100 The n-dimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional augmented cube AQn, an important variation of the hypercube, possesses several embedding properties that hypercubes and other variations do not possess. The advantages of AQn are that the diameter is only about half of the diameter of Qn and it is node-symmetric. Recently, some interesting properties of AQn have been investigated in the literature. The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the interconnection network. A network G contains one isometric path cover and is called isometric path coverable if for any two distinct pairs of nodes us, ut and vs, vt of G, there exist two node-disjoint paths P and Q satisfying that (1) P joins us and ut , and Q joins vs and vt , (2) |P| = |Q|, and (3) every node of G appears in P and Q exactly once. In this thesis, we first prove that the augmented cube AQn contains two edge-disjoint Hamiltonian cycles for n is equal or greater than 3. We then prove that AQn, with n is equal or greater than 2, is isometric path coverable. Based on the proofs of existences, we further present linear time algorithms to construct two edge-disjoint Hamiltonian cycles and one isometric path cover in an n-dimensional augmented cube AQn. Ruo-Wei Hung 洪若偉 2012 學位論文 ; thesis 40 en_US |
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碩士 === 朝陽科技大學 === 資訊工程系碩士班 === 100 === The n-dimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional augmented cube AQn, an important variation of the hypercube, possesses several embedding properties that hypercubes and other variations do not possess. The advantages of AQn are that the diameter is only about half of the diameter of Qn and it is node-symmetric. Recently, some interesting properties of AQn have been investigated in the literature. The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the interconnection network. A network G contains one isometric path cover and is called isometric path coverable if for any two distinct pairs of nodes us, ut and vs, vt of G, there exist two node-disjoint paths P and Q satisfying that (1) P joins us and ut , and Q joins vs and vt , (2) |P| = |Q|, and (3) every node of G appears in P and Q exactly once. In this thesis, we first prove that the augmented cube AQn contains two edge-disjoint Hamiltonian cycles for n is equal or greater than 3. We then prove that AQn, with n is equal or greater than 2, is isometric path coverable. Based on the proofs of existences, we further present linear time algorithms to construct two edge-disjoint Hamiltonian cycles and one isometric path cover in an n-dimensional augmented cube AQn.
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author2 |
Ruo-Wei Hung |
author_facet |
Ruo-Wei Hung Chun-Kai Wang 王俊凱 |
author |
Chun-Kai Wang 王俊凱 |
spellingShingle |
Chun-Kai Wang 王俊凱 Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
author_sort |
Chun-Kai Wang |
title |
Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
title_short |
Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
title_full |
Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
title_fullStr |
Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
title_full_unstemmed |
Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes |
title_sort |
two edge-disjoint hamiltonian cycles and one isometric path cover in augmented cubes |
publishDate |
2012 |
url |
http://ndltd.ncl.edu.tw/handle/10688943365551438099 |
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