A Cop and Drunken Robber Game on n -Dimensional Infinite-Grid Graphs

Nuttanon Songsuwan, Thiradet Jiarasuksakun, Anuwat Tangthanawatsakul and Pawaton Kaemawichanurat
Additional contact information
Nuttanon Songsuwan: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Thiradet Jiarasuksakun: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Anuwat Tangthanawatsakul: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Pawaton Kaemawichanurat: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

Mathematics, 2021, vol. 9, issue 17, 1-18

Abstract: A Cop and Drunken Robber (CDR) game is one variation of a famous combinatorial game, called Cops and Robbers, which has been extensively studied and applied in the area of theoretical and computer science as demonstrated by several conferences and publications. In this paper, for a natural number n , we present two strategies for a single cop to chase a drunken robber on n -dimensional infinite-grid graphs. Both strategies show that if the initial distance between the cop and the drunken robber is s , then the expected capture time is s + o ( s ) .

Keywords: random walks; pursuit evasion; cops and robbers; expected capture time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/17/2107/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/17/2107/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:17:p:2107-:d:626410

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().