2019 Fiscal Year Research-status Report
Using Containment Relations to Understand and Compute Width Parameters of Graphs
| Project/Area Number |
18K11157
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
BELMONTE Remy 電気通信大学, 大学院情報理工学研究科, 助教 (80780147)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | Width parameters / Reconfiguration / Parameterized complexity / Structural parameters |
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| Outline of Annual Research Achievements |
Over the last year, we have obtained the following results in relation with the project :
- Independent set reconfiguration parameterized by modular-width. Joint work with Tesshu Hanaka, Michael Lampis, Hirotaka Ono and Yota Otachi. We studied the parameterized complexity of the independent set reconfiguration problem. These results appeared in the proceedings of WG 2019.
- Tight complexity bounds for problems parameterized by rank-width. Joint work with Ignasi Sau. These results are accepted for publication at WG 2020.
Parameterized Complexity of (A, l)-Path Packing. Joint work with Tesshu Hanaka, Masaaki Kanzaki, Masashi Kiyomi, Yasuaki Kobayashi, Yusuke Kobayashi5, Michael Lampis, Hirotaka Ono, and Yota Otachi. These results are accepted for publication at IWOCA 2020.
- Covering edges with triangles. Joint work with Kyohei Chiba, Hiro Ito, Atsuki Nagao, Michael Lampis and Yota Otachi. These results are submitted for journal publication.
- Parameterized complexity of Grundy Coloring (completed). Joint work with Tesshu Hanaka, Eun-Jung Kim, Michael Lampis, Hirotaka Ono, Yota Otachi and Florian Sikora. These results are accepted for publication at ESA 2020.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
While some structural insight into the relationship between certain specific problems (parity variants of classical problems in particular) and width parameters for dense graphs (in particular clique-width) were obtained, the main goal of studying the interplay between those width parameters and specific containment relations has eluded our efforts. We hope to obtain more conclusive results in the remaining years of this project.
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| Strategy for Future Research Activity |
We plan to pursue the lines of research initiated thus far, i.e., the study of the interplay between various algorithmic problems and width-parameters for dense graphs. Through this approach, we hope to gain further insight into the behavior of those very parameters. In addition, we will turn to algorithmic aspects of certain specific containment relations, e.g., vertex minors. By combining those two approaches, we hope to make significant steps towards the main goal of this project: computing width parameter decompositions through containment relations.
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| Causes of Carryover |
Due to the onset of the Covid-19 pandemic in January and the ensuing travel restrictions imposed by the Japanese government in February and March this year, I was unable to spend the full amount of last fiscal year's funding. The research visits that were cancelled as a result will be performed during this fiscal year instead, provided the healthcare crisis and travel restrictions are resolved.
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