A study on reconfiguration problems under Token Sliding and their applications
Project/Area Number 
19K24349

Research Category 
GrantinAid for Research Activity Startup

Allocation Type  Multiyear Fund 
Review Section 
1001:Information science, computer engineering, and related fields

Research Institution  Kyushu Institute of Technology 
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)

Project Period (FY) 
20190830 – 20210331

Project Status 
Granted (Fiscal Year 2019)

Budget Amount *help 
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)

Keywords  reconfiguration problem / kpath vertex cover / computational complexity / PSPACEcomplete / polynomial time / token sliding / graph algorithms 
Outline of Research at the Start 
Recently, reconfiguration problems involving the socalled Token Sliding rule has been used for modeling many realworld problems. Usually, each vertex of a given graph contains a token, and one can move/slide a token from one vertex to one of its unoccupied neighbors. Typically, one is asked if it is possible to "reconfigure" one tokenset into another by repeatedly applying this sliding operation. This research aims to explore the computational complexities of reconfiguration problems under Token Sliding in different settings, and derive useful knowledge of P, NP, and PSPACE along the way.

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 kpath vertex cover (kPVC) of a graph G is a vertexsubset I of G such that each path in G having k vertices contains at least one member of I. This kPVC concept has potential applications in different areas. We initiate the study of different reconfiguration variants of kPVC under TS and some other rules. We showed the PSPACEhardness 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.

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 PSPACEhard, and even with restricted settings in which they can be solved in polynomial time, the corresponding algorithms are technically nontrivial. The achievements of the first year include one peerreviewed paper (initiating the study of reconfiguration variants of a wideapplicable graph problem) and one presentation at international conferences. As a result, the project goes rather smoothly as planned.

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 “tokenmoving” 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.

Report
(1 results)
Research Products
(2 results)