Markov Models for the Tipsy Cop and Robber Game on Graph

Viktoriya Bardenova, Vincent Ciarcia, Erik Insko
{"title":"Markov Models for the Tipsy Cop and Robber Game on Graph","authors":"Viktoriya Bardenova, Vincent Ciarcia, Erik Insko","doi":"10.4236/ojdm.2021.113006","DOIUrl":null,"url":null,"abstract":"In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level though the duration of the game; the second is when the cop and robber sober up as a function of time; the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through $\\mathbf{M}$ rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/ojdm.2021.113006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level though the duration of the game; the second is when the cop and robber sober up as a function of time; the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through $\mathbf{M}$ rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
图上醉酒警察和强盗游戏的马尔可夫模型
本文分析和建模了Harris、Insko、Prieto-Langarica、Stoisavljevic和Sullivan在2020年提出的三个关于图上微醺警察和强盗博弈的开放问题。我们模拟的三种不同的情景说明了不同的生物学情景。第一种情况是,在整个游戏过程中,警察和抢劫犯的醉酒程度始终如一;第二个是警察和抢劫犯清醒的时间函数;第三个是警察和强盗清醒的时间,这是他们之间距离的函数。使用马尔可夫链对每个场景建模,我们计算了游戏持续到$\mathbf{M}$回合的概率,以及给定警察和强盗不同的起始位置和醉酒水平的预期游戏长度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
127
期刊最新文献
Genome Sequencing Using Graph Theory Approach A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials A Novel Design Method for Protein-Like Molecules from the Perspective of Sheaf Theory Solving the k-Independent Sets Problem of Graphs by Gröbner Bases Rupture Degree of Some Cartesian Product Graphs
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1