A study on reconfiguration problems under Token Sliding and their applications

• Project/Area Number: 19K24349
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year 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): 2019-08-30 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥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 problems / token sliding / k-path vertex cover / graph algorithms / reconfiguration graph / reconfiguration problem / computational complexity / PSPACE-complete / polynomial time

Outline of Research at the Start

Recently, reconfiguration problems involving the so-called Token Sliding rule has been used for modeling many real-world 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 token-set 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 Final Research Achievements

In a Token Sliding (TS) reconfiguration problem, each configuration is a set of tokens placed on vertices of a graph G, and two token-sets are adjacent if one can be obtained from the other via a single token-slide from an occupied vertex to one of its neighbors. In this research, we initiated the study of some reconfiguration variants of this problem under TS and some other rules, where each token-set forms a k-path vertex cover (k-PVC) of G, i.e., each path on k vertices of G has at least one token. We succeeded in determining whether they are easy/hard to solve for different graph classes. The k-PVC concept arises when designing certain secured sensor networks. This research may be useful when we want to slightly change the network while keeping its secured property.

Academic Significance and Societal Importance of the Research Achievements

When designing certain networks, one needs to put a "secured" device on each path on k vertices of the communication graph. Our results may be useful in situations where one needs to reconfigure the networks without changing its security.

Research Products

• [Journal Article] Reconfiguring k-path Vertex Covers (2020)
  • Author(s): Hoang Duc A.、Suzuki Akira、Yagita Tsuyoshi
  • Journal Title: Proceedings of the 14th International Conference and Workshop on Algorithms and Computation, WALCOM 2020 Volume: LNCS 12049 Pages: 133-145
  • DOI: 10.1007/978-3-030-39881-1_12
  • ISBN: 9783030398804, 9783030398811
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Reconfiguring k-Path Vertex Covers (2020)
  • Author(s): Duc A. Hoang, Akira Suzuki, Tsuyoshi Yagita
  • Organizer: The 14th International Conference and Workshop on Algorithms and Computation, WALCOM 2020