Markov Models for the Tipsy Cop and Robber Game on Graph  

作　　者：Viktoriya Bardenova Vincent Ciarcia Erik Insko Viktoriya Bardenova;Vincent Ciarcia;Erik Insko(Florida Gulf Coast University, Fort Myers, Florida)

机构地区：[1]Florida Gulf Coast University, Fort Myers, Florida

出　　处：《Open Journal of Discrete Mathematics》2021年第3期61-93,共33页离散数学期刊（英文）

摘　　要：<span style="font-family:Verdana;">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 through 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 <strong>M</strong> rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.</span><span style="font-family:Verdana;">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 through 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 <strong>M</strong> rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.</span>

关 键 词：Cops and Robbers Graph Searching Markov Chains 

分 类 号：TB6[一般工业技术—制冷工程]