A study on reconfiguration problems under Token Sliding and their applications

2020 Fiscal Year Final Research Report

• 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
• Keywords: reconfiguration problems / token sliding / k-path vertex cover / graph algorithms

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.

Free Research Field

Graph Algorithms

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.