Optimizing periodic patrols against short attacks on the line and other networks

Abstract

We consider a patrolling game on a graph recently introduced by Alpern et al. (2011) where the Patroller wins if he is at the attacked node while the attack is taking place. This paper studies the periodic patrolling game in the case that the attack duration is two periods. We show that if the Patroller's period is even, the game can be solved on any graph by finding the fractional covering number and fractional independence number of the graph. We also give a complete solution to the periodic patrolling game on line graphs of arbitrary size, extending the work of Papadaki et al. (2016) to the periodic domain. This models the patrolling problem on a border or channel, which is related to a classical problem of operational research going back to Morse and Kimball (1951). A periodic patrol is required to start and end at the same location, for example the place where the Patroller leaves his car to begin a foot patrol.

Adversarial Patrolling in a Uniform

“…Earlier work on patrolling a channel/border with different paradigms, includes Washburn (1982Washburn ( , 2010, Szechtman et al (2008), Zoroa N, Fernández-Sáez andZoroa P (2012), andCollins et al (2013). The case of a Patroller restricted to periodic walks has been studied by Alpern, Lidbetter and Papadaki (2019). The related problem of ambush is studied by Kikuta (2004, 2009).…”

Technical Note—Optimal Patrol of a Perimeter

“…Lin et al (2013) extends the work to allow random attack times, and Lin et al (2014) further accounts for the possibility of overlook. Papadaki et al (2016) and Alpern et al (2019) study a similar formulation but focus on the border patrol, while McGrath and Lin (2017) consider how to coordinate multiple patrollers. In these works, the attacker cannot see the patroller.…”

The Uniformed Patroller Game

“…Earlier work on patrolling a channel/border with different paradigms, includes Washburn (1982Washburn ( , 2010, Szechtman et al (2008), Zoroa N, Fernández-Sáez andZoroa P (2012), andCollins et al (2013). The case where the Patroller is restricted to periodic walks has recently been studied by Alpern, Lidbetter and Papadaki (2019). The related problem of ambush is studied by Kikuta (2004, 2009), while an artificial intelligence approach to patrolling is given by Basilico, Gatti and Amigoni (2012).…”