2019 Fiscal Year Research-status Report
A study on reconfiguration problems under Token Sliding and their applications
| Project/Area Number |
19K24349
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
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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| Project Period (FY) |
2019-08-30 – 2021-03-31
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| Keywords | reconfiguration problem / k-path vertex cover / computational complexity / PSPACE-complete / polynomial time |
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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| Causes of Carryover |
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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Research Products
(2 results)
