2006 Fiscal Year Final Research Report Summary
The Research for Finding Algorithms to Solve Some Combination Problems on Partial k-Trees
| Project/Area Number |
16500002
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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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, 大学院・情報科学研究科, 助教授 (10272022)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIZEKI Takao Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (80005545)
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| Project Period (FY) |
2004 – 2006
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| Keywords | algorithm / partial k-tree / tree-decomposition / coloring |
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| Research Abstract |
In a field of a computational complexity theory and algorithm theory, various combination problems on graphs have been studied. It is known that the most of such problems, including a lot of practical problems, are NP-hard. On the other hand, it is known that some of these problems can be solved in polynomial time for restricted classes of graphs, named partial k-trees. However, in my best knowledge there exist polynomial-time algorithms for solving some particular problems on partial k-trees and no general methods for it. In this research, I investigated existing algorithms for partial k-trees and find some algorithms to solve some combination problems of a part k tree including a [g, f]-coloring algorithm, a multiple coloring algorithm, a cost coloring algorithm, etc. It succeeded to find some conditions for solving some combination optimization and building the methodology that could generate efficient algorithm to solve those problems automatically. Furthermore, for a small k, say one (trees) or two (series-parallel graphs), it succeeded to develop polynomial-time algorithm for solving cost coloring problem, multiple coloring problem, etc. Inspection of effectiveness of the technique was possible theoretically. In this research, I have published 17 journal papers and 20 international conference papers. As a result of having been provided, I give many linear-time algorithms. Its impact in a field of a linear-time algorithm theory is very big.
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