| 研究課題/領域番号 |
19K24349
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| 研究機関 | 九州工業大学 |
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研究代表者 |
DucA. Hoang 九州工業大学, 大学院情報工学研究院, 博士研究員 (00847824)
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| 研究期間 (年度) |
2019-08-30 – 2021-03-31
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| キーワード | reconfiguration problem / k-path vertex cover / computational complexity / PSPACE-complete / polynomial time |
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| 研究実績の概要 |
This project aims to investigate the (in)tractability of different reconfiguration problems under Token Sliding (TS), which may hopefully derive useful knowledge of P, NP, and PSPACE. A k-path vertex cover (k-PVC) of a graph G is a vertex-subset I of G such that each path in G having k vertices contains at least one member of I. This k-PVC concept has potential applications in different areas. We initiate the study of different reconfiguration variants of k-PVC under TS and some other rules. We showed the PSPACE-hardness of these variants for planar and bounded bandwidth graphs of maximum degree 3, bipartite graphs, and chordal graphs. On the positive side, we designed efficient algorithms for solving some variants on paths, cycle, trees. We presented these results at WALCOM 2020.
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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
As mentioned in the outline of this research, we aim to study reconfiguration problems under Token Sliding (TS) and related models in different settings. In general, most reconfiguration problems under TS (as well as many other rules) are PSPACE-hard, and even with restricted settings in which they can be solved in polynomial time, the corresponding algorithms are technically non-trivial. The achievements of the first year include one peer-reviewed paper (initiating the study of reconfiguration variants of a wide-applicable graph problem) and one presentation at international conferences. As a result, the project goes rather smoothly as planned.
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| 今後の研究の推進方策 |
This project aims to investigate the (in)tractability of different reconfiguration problems under Token Sliding (TS), which may hopefully derive useful knowledge of P, NP, and PSPACE. Toward this goal, we are going to: (1) tackle different reconfiguration variants to see which structural property of a problem makes it easy/hard to solve under TS; (2) consider reconfiguration problems whose reconfiguration rule relates to “moving tokens on graphs” to see why the problems under TS are easier/harder than other “token-moving” rules; and (3) study different “types” of
TS rule, for instance, by allowing multiple tokens to be simultaneously moved, or by restricting that only certain tokens can be moved, and so on.
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| 次年度使用額が生じた理由 |
In the next fiscal year, the grant will be used mostly for business trips (attending conferences, collaboration, etc.) and equipment. I will spend around 600000 yen for business trips, 300000 yen for buying equipment (PC, books, etc.), and the remaining of the grant for other miscellaneous stuff.
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