Abstract
Patrolling and surveillance games both deal with a chasing-evading situation of an adversary trying to escape detection by either a mobile defender (patrolling) or a fixed defender (surveillance). Both kinds of games are played on graphs as abstract models of an infrastructure, and we review a variety of closed-form solutions for optimal patrolling in different classes of graph topologies. Applications include patrolling along lines (borders, pipelines, or similar), harbors (tree-structured graphs), and large geographic areas in general (planar graphs and maps). For surveillance and patrolling, we give hints on how to estimate the necessary resources, and how to include imperfectness and uncertainty, related to the detection capabilities, but also the chances of the adversary escaping the view of the patroller or surveillance. In complex terrain, we will discuss the use of simulation and empirical games (over real-valued and stochastic orders).
Under observation, we act less free, which means we effectively are less free. E. Snowden
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alonso NZ, Terol PZ (1993) Some games of search on a lattice. Naval Res Logist 40(4):525–541. https://doi.org/10.1002/1520-6750(199306)40:4<525::AID-NAV3220400407>3.0.CO;2-B
Alpern S, Asic M (1985) The search value of a network. Networks 15(2):229–238. https://doi.org/10.1002/net.3230150208
Alpern S, Fokkink R (2014) Accumulation games on graphs. Networks 64(1):40–47. https://doi.org/10.1002/net.21555
Alpern S, Fokkink R, Kikuta K (2010) On Ruckle’s conjecture on accumulation games. SIAM J Control Optim 48(8):5073–5083. https://doi.org/10.1137/080741926
Alpern S, Morton A, Papadaki K (2011) Patrolling games. Oper Res 59(5):1246–1257. https://doi.org/10.1287/opre.1110.0983
Alpern S, Lidbetter T, Morton A, Papadaki K (2016) Patrolling a pipeline. In: Zhu Q, Alpcan T, Panaousis E, Tambe M, Casey W (eds) Decision and game theory for security. Lecture notes in computer science. Springer International Publishing, Cham, pp 129–138
Alpern S, Lidbetter T, Papadaki K (2017) Periodic patrols on the line and other networks. ArXiv:1705.10399v1 [math.OC]
Appel K, Haken W (1989) Every planar map is four colorable, vol 98. American Mathematical Society, Providence. https://doi.org/10.1090/conm/098
Basak A, Fang F, Nguyen TH, Kiekintveld C (2016) Combining graph contraction and strategy generation for green security games. In: Zhu Q, Alpcan T, Panaousis E, Tambe M, Casey W (eds) Decision and game theory for security. Lecture notes in computer science. Springer International Publishing, Cham, pp 251–271
Bodor R, Drenner A, Schrater P, Papanikolopoulos N (2007) Optimal camera placement for automated surveillance tasks. J Intell Robot Syst 50(3):257–295. https://doi.org/10.1007/s10846-007-9164-7
Chvátal V (1975) A combinatorial theorem in plane geometry. J Combin Theory Ser B 18:39–41
Cormen TH, Leiserson CE, Rivest RL (1994) Introduction to algorithms. MIT Press, Cambridge
Debaque B, Jedidi R, Prevost D (2009) Optimal video camera network deployment to support security monitoring. In: 12th international conference on information fusion, 2009. IEEE, Piscataway, pp 1730–1736
Edmonds J, Johnson EL (1973) Matching, Euler tours and the Chinese postman. Math Program 5(1):88–124. https://doi.org/10.1007/BF01580113
Fisk S (1978) A short proof of Chvátal’s Watchman theorem. J Combin Theory Ser B 24(3):374. https://doi.org/10.1016/0095-8956(78)90059-X
Fox CR, Bardolet D, Lieb D (2005) Partition dependence in decision analysis, resource allocation, and consumer choice. In: Zwick R, Rapoport A (eds) Experimental business research. Springer, Dordrecht/Berlin, pp 229–251. https://doi.org/10.1007/0-387-24244-9_10
Garey MR, Johnson DS (1979) Computers and intractability. Freeman, New York
Hörster E, Lienhart R (2006) On the optimal placement of multiple visual sensors. In: Aggarwal JK, Cucchiara R, Prati A (eds) Proceedings of the 4th ACM international workshop on video surveillance and sensor networks – VSSN’06, p 111. ACM Press, New York. https://doi.org/10.1145/1178782.1178800
Indu S, Chaudhury S, Mittal N, Bhattacharyya A (2009) Optimal sensor placement for surveillance of large spaces. In: 2009 third ACM/IEEE international conference on distributed smart cameras (ICDSC). IEEE, pp 1–8. https://doi.org/10.1109/ICDSC.2009.5289398
Kikuta K, Ruckle WH (2002) Continuous accumulation games on discrete locations. Naval Res Logist 49(1):60–77. https://doi.org/10.1002/nav.1048
O’Rourke J (1987) Art gallery theorems and algorithms. The international series of monographs on computer science, vol 3. Oxford University Press, New York
Papadaki K, Alpern S, Lidbetter T, Morton A (2016) Patrolling a border. Oper Res 64(6):1256–1269. https://doi.org/10.1287/opre.2016.1511
Pita J, Tambe M, Kiekintveld C, Cullen S, Steigerwald E (2011) GUARDS – innovative application of game theory for national airport security. In: IJCAI 2011, pp 2710–2715 . https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-451
Rass S, Alshawish A, Abid MA, Schauer S, Zhu Q, de Meer H (2017) Physical intrusion games – optimizing surveillance by simulation and game theory. IEEE Access 5:8394–8407. https://doi.org/10.1109/ACCESS.2017.2693425
Rass S, König S, Schauer S (2017) On the cost of game playing: how to control the expenses in mixed strategies. In: Decision and game theory for security. Springer, Cham, Switzerland [S.l.], pp 494–505
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Rass, S., Schauer, S., König, S., Zhu, Q. (2020). Patrolling and Surveillance Games. In: Cyber-Security in Critical Infrastructures. Advanced Sciences and Technologies for Security Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-46908-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-46908-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-46907-8
Online ISBN: 978-3-030-46908-5
eBook Packages: Computer ScienceComputer Science (R0)