2001 Fiscal Year Final Research Report Summary
A Method for solving scheduling problems by graph algorithms
| Project/Area Number |
10205201
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | Tohoku University |
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Principal Investigator |
ZHOU Xiao Tohoku University, Graduate School of Information Sciences, Associate Professor, 情報科学研究科, 助教授 (10272022)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUKI Takaaki Tohoku University, Information Synergy Center, Associate Professor, ネットワーク研究部, 助教授 (90323089)
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)
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| Project Period (FY) |
1998 – 2000
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| Keywords | graph / algorithm / edge-coloring / total coloring / cost edge-coloring / 1-vertex-coloring / [g, f]-coloring |
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| Research Abstract |
The scheduling problem was modeled by using the graph in this research. It is well-known that the coloring problem, from which the application to this problem is strongly expected, is NP-hard 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 k-trees 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 k-trees which is published in ISAAC' 99. Afterwards, we improved it for degenerate graphs which is published in ICALP' 01.
3. We gave a polynomial-time algorithm to solve the 1-vertex-coloring problem for partial k-trees which is published in IEICE Trans. on fundamentals of Electronics, Communication and Computer Science (2000).
4. We give a polynomial-time algorithm to solve the cost edge-coloring problem for trees which is published in COCOON' 01.
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