'We will go wherever they hide': Rooting out IS in Somalia A figure appears in the picture, moving through a valley. He has been to fetch water for his friends, says the drone operator. He is running and carrying something on his back, adds another soldier. The man on the screen is near a cave, which the army believes is a hideout for 50 to 60 IS fighters. The Puntland Defence Forces have about 500 soldiers stationed at this base in the north-east of Somalia. Ten years ago the barren and inhospitable landscape was home to only a few nomadic communities, but that changed when IS established a foothold here, shifting its focus to Africa as its fighters were driven out of their strongholds in Syria and Iraq.

A number of real-world security scenarios can be cast as a problem of transiting an area guarded by a mobile patroller, where the transiting agent aims to choose its route so as to minimize the probability of encountering the patrolling agent, and vice versa. We model this problem as a two-player zero-sum game on a graph, termed the transit game. In contrast to the existing models of area transit, where one of the players is stationary, we assume both players are mobile. We also explicitly model the limited endurance of the patroller and the notion of a base to which the patroller has to repeatedly return. Noting the prohibitive size of the strategy spaces of both players, we develop single- and double-oracle based algorithms including a novel acceleration scheme, to obtain optimum route selection strategies for both players. We evaluate the developed approach on a range of transit game instances inspired by real-world security problems in the urban and naval security domains.