Using Containment Relations to Understand and Compute Width Parameters of Graphs
Project/Area Number |
18K11157
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 60010:Theory of informatics-related
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Research Institution | The University of Electro-Communications |
Principal Investigator |
BELMONTE Remy 電気通信大学, 大学院情報理工学研究科, 助教 (80780147)
|
Project Period (FY) |
2018-04-01 – 2021-03-31
|
Project Status |
Discontinued (Fiscal Year 2020)
|
Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
Keywords | Parameterized algorithms / Graphs / Width parameters / Reconfiguration / Parameterized complexity / Structural parameters / Algorithms / Containment relations |
Outline of Annual Research Achievements |
As a result of this project, we have obtained a wide variety of algorithmic, complexity theoretic and graph theoretic results, in particular from the point of view of parameterized complexity and width parameters. Some highlights of the results obtained during the project include solving the computation complexity of the Independent Set Reconfiguration problem for the token sliding rule on split graph, which was a long-standing open problem, and identifying the first problem that distinguishes treewidth from path-width from the point of view of parameterized tractability, namely Grundy coloring. Together, the results we obtained help refine understanding of the complexity landscape of various fundamental graph-theoretic computational problems, especially from the point of view of width-parameters. We also obtained other various results, such as an in-depth study of the classical and parameterized complexity of finding large odd subgraphs and odd colorings of graphs. In particular, we studied the parameterized complexity of such problems under the graphs parameter rank-width, and proved that those problems can be solved in single-exponential time when parameterized by rank-width, the first problems shown to have this property. This distinguise those problems from their classical, non-parity variants, which, as far as current knowledge goes, require super-exponential running-time to be solved. We hope these results will pave the way to a better understanding of the differences between rank-width and clique-width (a parameter closely related to rank-width).
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Report
(3 results)
Research Products
(18 results)