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— This paper addresses the solution of large zero-sum matrix games using randomized methods. We provide a procedure by which a player can compute mixed policies that, with high probability, are security policies against an adversary that is also using randomized methods to solve the game. The computational savings result from solving subgames that are much… (More)

We address discrete-time pursuit-evasion games in the plane where every player has identical sensing and motion ranges restricted to closed discs of given sensing and stepping radii. A single evader is initially located inside a bounded subset of the environment and does not move until detected. We propose a Sweep-Pursuit-Capture pursuer strategy to capture… (More)

We introduce a problem in which demands arrive stochastically on a line segment, and upon arrival, move with a fixed velocity perpendicular to the segment. We design a receding horizon service policy for a vehicle with speed greater than that of the demands, based on the translational minimum Hamiltonian path (TMHP). We consider Poisson demand arrivals,… (More)

We address a pursuit-evasion problem involving an unbounded planar environment, a single evader and multiple pursuers moving along curves of bounded curvature. The problem amounts to a multi-agent version of the classic homicidal chauffeur problem; we identify parameter ranges in which a single pursuer is not sufficient to guarantee evader capture. We… (More)

— We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to… (More)

—We consider the problem of dynamic vehicle routing under exact time constraints on servicing demands. Demands for service are generated in an environment as follows: uniformly randomly in space and Poisson in time. Every demand needs to be serviced exactly after a fixed, finite interval of time after it is generated. We design routing policies for a… (More)

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a… (More)

We address optimal placement of vehicles with simple motion, to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target either moves with fixed speed and in a fixed direction or… (More)

—We address a discrete-time, pursuit-evasion game with alternate moves played between two kinds of players: the pursuer and the evader. The pursuer wishes to capture the evader while the evader's goal is to avoid capture. By capture, we mean that the distance between the players is no greater than 1 unit. We assume simple, first-order motion kinematics for… (More)