Hypergraph Drawing with Backbones

• Main Authors: Hsuan-Yin Tsai, 蔡萱尹
• Other Authors: Hsu-Chun Yen
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/56201238766778265404

碩士 === 國立臺灣大學 === 電機工程學研究所 === 103 === The thesis mainly discusses various optimization problems with respect to three aesthetic criteria in hypergraph drawings under the condition that each hyperedge has one backbone. The aesthetic criteria include minimizing the number of crossings, the total hyperedge length, and maximizing the number of hyperedges under the condition that a hypergraph has no overlapping hyperedge. In the aspect of crossings minimization, if there is an order among the hyperedges, we can use a dynamic programming algorithm to solve it. In the aspect of total length minimization, we transform the problem into the bipartite matching problem to solve it. In the aspect of maximizing the number of hyperedges, a greedy algorithm is proposed. Also, the thesis considers three different types of backbones: with horizontal backbones only, with both horizontal and vertical backbones, and allowing horizontal, vertical and octilinear horizontal backbones.