研究生: |
陳政謙 Cheng-Chien Chen |
---|---|
論文名稱: |
極大外平面圖上之距離監視問題 Distance Guarding Problem in Maximal Outerplanar Graphs |
指導教授: |
王有禮
Yue-Li Wang |
口試委員: |
徐俊傑
Chiun-Chieh Hsu 吳若禹 Ro-Yu Wu |
學位類別: |
碩士 Master |
系所名稱: |
管理學院 - 資訊管理系 Department of Information Management |
論文出版年: | 2016 |
畢業學年度: | 104 |
語文別: | 英文 |
論文頁數: | 22 |
中文關鍵詞: | 距離k監視問題 、距離k監視集合 、極大外平面圖 |
外文關鍵詞: | kd-guarding problem, kd-guarding set, maximal outerplanar graphs |
相關次數: | 點閱:157 下載:1 |
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給定一個平面圖G,圖G上的一個內平面f 可以被一個點p距離k可見的條件為點p到平面f 的 邊界上一點x的距離小於等於k − 1。 一組在圖G上的距離k監視集合S為一組點集合使得圖G上 的每一個內平面都可以被S集合中的點距離k可見。 在本篇論文中,我們設計了一個線性時間 的演算法在極大外平面圖上找最小之距離2監視集合。
Given a planar graph G = (V, E), we say that an inner face f of G is kd-visible from a vertex p ∈ V if there is a vertex x in the boundary of f such that dG(x,p) k − 1, where dG(p,x) is the length of a shortest path from p to x. A kd-guarding set of G is a subset S ⊆ V such that every face of G is kd-visible from some vertex in S. In this thesis, we show that finding a minimal 2d-guarding set of a maximal outerplanar graph can be solved in linear time.
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