Computing k-vertex Connectivity and Disjoint s-t Paths on Permutation Graphs

• Main Authors: Yi-Wen Chen, 陳儀文
• Other Authors: Shi-Jinn Horng
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/99702755546761759037

碩士 === 國立臺灣科技大學 === 電機工程研究所 === 82 === In this thesis, we shall present several algorithms for determining the maximum number of vertex connectivity, testing k-vertex connectivity, determining the maximum number of vertex disjoint s-t paths and finding k-vertex disjoint s-t paths problems on a permutation graph, respectively. We first give several O(n ** 2) time sequential algorithms for determining the maximum number of vertex connectivity, testing k-vertex connectivity and determining the maximum number of vertex disjoint s-t paths problems, respectively. Then, an O(k n ** 2) time algorithm for finding k-vertex disjoint s-t paths problem on a permutation graph is also proposed. Moreover, we also derive the corresponding parallel algorithms for these problems from the proposed sequential algorithms. On the EREW PRAM model , we first propose several O(log n) time optimal speed-up parallel algorithms for determining the maximum number of vertex connectivity, testing k-vertex connectivity and determining the maximum number of vertex disjoint s-t paths problems, all with O(n ** 2 / log n) processors, respectively. Then, an O(n log n) parallel algorithm for finding k-vertex disjoint s-t paths problem using O(n ** 2 / log n) processors is also developed, where k is a fixed integer.