Patrolling a border

Katerina Papadaki, Steve Alpern, Thomas Lidbetter, Alec Morton

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
23 Downloads (Pure)


Patrolling games were recently introduced by Alpern, Morton and Papadaki to model the problem of protecting the nodes of a network from an attack. Time is discrete and in each time unit the Patroller can stay at the same node or move to an adjacent node. The Attacker chooses when to attack and which node to attack, and needs m consecutive time units to carry it out. The Attacker wins if the Patroller does not visit the chosen node while it is being attacked; otherwise the Patroller wins. This paper studies the patrolling game where the network is a line graph of n nodes, which models the problem of guarding a channel or protecting a border from infiltration. We solve the patrolling game for any values of m and n, providing an optimal Patroller strategy, an optimal Attacker strategy and the value of the game (optimal probability that the attack is intercepted).
Original languageEnglish
Pages (from-to)1256–1269
Number of pages15
JournalOperations Research
Issue number6
Publication statusPublished - 12 Sep 2016


  • search and surveillance
  • patrolling
  • patrolling games
  • game theory


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