Project/Area Number  10205201 
Research Category 
GrantinAid for Scientific Research on Priority Areas (B).

Research Institution  Tohoku University 
Principal Investigator 
ZHOU Xiao Tohoku University, Graduate School of Information Sciences, Associate Professor, 情報科学研究科, 助教授 (10272022)

CoInvestigator(Kenkyūbuntansha) 
KUSAKARI Yishiyoki Akita Prefectural University, Department of Electronics and Information Systems, Lecturer, システム科学技術学部・電子情報システム学科, 講師 (50302203)
MIZUKI Takaaki Tohoku University, Information Synergy Center, Associate Professor, ネットワーク研究部, 助教授 (90323089)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2001)

Budget Amount *help 
¥10,700,000 (Direct Cost : ¥10,700,000)
Fiscal Year 2000 : ¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1999 : ¥3,600,000 (Direct Cost : ¥3,600,000)
Fiscal Year 1998 : ¥4,500,000 (Direct Cost : ¥4,500,000)

Keywords  graph / algorithm / edgecoloring / total coloring / cost edgecoloring / 1vertexcoloring / [g, f]coloring / グラフ / アルゴリズム / 辺彩色 / 全彩色 / コスト辺彩色 / 1点彩色 / [g,f]辺彩色 / 点彩色 / 金彩色 / 部分kホ / 辺ランク / ランク付け / 辺ランク付け / 彩色問題 
Research Abstract 
The scheduling problem was modeled by using the graph in this research. It is wellknown that the coloring problem, from which the application to this problem is strongly expected, is NPhard in general. So it is very unlikely that there exists an efficient algorithm to solve it. However, we showed that the problem can be solved efficiently for some restricted class of graphs. The results achieved for this research are chiefly four of the following. 1. We gave a linear algorithm to solve [g, f]coloring problem for partial ktrees by a dynamic programming method. This result was published in Algorithmica(1999). 2. We give a linear algorithm to solve the total coloring problem for partial ktrees which is published in ISAAC' 99. Afterwards, we improved it for degenerate graphs which is published in ICALP' 01. 3. We gave a polynomialtime algorithm to solve the 1vertexcoloring problem for partial ktrees which is published in IEICE Trans. on fundamentals of Electronics, Communication and Computer Science (2000). 4. We give a polynomialtime algorithm to solve the cost edgecoloring problem for trees which is published in COCOON' 01.
