| 研究実績の概要 |
Over the course of the previous fiscal year, the following results have been obtained as part of the project, and have been published in international, peer-reviewed conferences:
- We studied the Colorable Set Reconfiguration problem on split and chordal graphs, under the token sliding rule. In particular, we solved an open problem in the area of combinatorial reconfiguration by proving that Independent Set Reconfiguration (equivalently, 1-Colorable Set Reconfiguration) remains PSPACE-complete on split graphs. We also showed that Colorable Set Reconfiguration can be solved efficiently on chordal graphs, for any number of colors other than 1. These results were published at STACS 2019.
- We studied the parameterized complexity of computing a smallest safe set, a recently introduced measure of a graph's "robustness", under various structural parameterizations, such as pathwidth and clique-width. In particular, the problem is FPT when parameterized by neighborhood diversity, but not when parameterized by pathwidth, and this lower bound is essentially tight when parameterized by clique-width. These results were published at CIAC 2019.
- We proved that Independent Set Reconfiguration is fixed-parameter tractable when parameterized by modular-width, under all three standard reconfiguration rules. These results have been accepted for publication at WG 2019.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
While the amount and quality of results obtained so far has been high, they mostly pertain to purely algorithmic use of width parameters, rather than their structural study for computational purpose, which forms the main purpose of this project. Some of my current projects aim at correcting this status (see Future Work section below). However, it is important to note that those problems are notoriously difficult to tackle.
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| 今後の研究の推進方策 |
I am currently working on the following ongoing projects:
- The complexity of parity variants of classical problems on graphs of bounded rank-width. In particular, we consider variants of the well-known odd subgraph conjecture on graphs of bounded rank-width.
- The parameterized complexity of Grundy coloring, where one seeks to compute a worst-case, greedy, proper coloring of a graph. We study the problem under several parameterizations, such as clique-width, pathwidth and tree-depth.
I am also working on problems related to computing width parameters such as clique-width by making use of containment relations, such as identifying induced subgraph obstruction sets for graphs of bounded clique-width on some restricted classes of graphs.
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