Ear Decomposition Problem on Cactus Graphs

• Main Authors: CHENG WEN PIN, 鄭文濱
• Other Authors: 王有禮
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/98979495370969336600

碩士 === 國立臺灣科技大學 === 資訊管理系 === 88 === In this paper, we study the ear decomposition problem with bounds on ear length, and propose our algorithms for solving different kinds of ear decomposition problems in cactus graphs. There are four kinds of ear decomposition problems. They are short-ear decomposition(SED), long-ear decomposition(LED), strong short-ear decomposition (SSED) and strong long-ear decomposition(SLED). We shall focus on the SED problem on cactus graphs. Our work is divided into four parts. Firstly, we investigate the tree-like cactus graphs, and propose an O(m) algorithm to solve the SED problem, where m is the number of edges in a given graph. Secondly, we investigate the cactus graphs consist of cyclic blocks only, and propose another algorithm, which also takes O(m) time to recognize SED in such cactus graphs. Thirdly, we investigate the graphs consist of cyclic blocks and K2 blocks. We propose the third algorithm, which takes O(m) time, to decide the existence of SED in this kind of cactus graphs. Finally, we propose an O(m) algorithm to solve the SED problem for general cactus graph. As for the LED, SSED and SLED problems in cactus graphs, instead of detail investigation, we include the generalized algorithms for solving such problems in our conclusion. The time complexity of these algorithms is also O(m).