Computing Connected Components and Its Applications on an Interval Graph

• Main Authors: Horng-Ren Tsai, 蔡鴻仁
• Other Authors: Shi-Jinn Horng
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/48963573897510758830

碩士 === 國立臺灣科技大學 === 工程技術研究所 === 81 === In this thesis, we shall present several algorithms to solve the connected components problem, the transitive closure problem and the all-pair shortest path problem on an interval graph, respectively. We first give an O(n*log n) and an O(n**2) optimal time algorithms to compute the connected components and the transitive closure on an interval graph, respectively. Then, an O(n**2) optimal time algorithm for solving the all- pair shortest path problem on an interval graph is proposed. Those algorithms proposed in this paper are suitable to be implemented on parallel computation models. On the EREW PRAM model, we first propose an O(log n) time optimal parallel algorithm for each problem, each with O(n), O(n**2/log n) and O( n**2/log n) processors, respectively. Then, an O(1) step algorithm for each of these problems is also developed on the reconfigurable array of processors, each with O(n**2), O(n**2) and O(n**3) processors , respectively.