Efficient solutions to some transportation problems with applications to minimizing robot arm travel
SIAM Journal on Computing
Preemptive ensemble motion planning on a tree
SIAM Journal on Computing
Nonpreemptive ensemble motion planning on a tree
Journal of Algorithms
Routing a vehicle of capacity greater than one
Discrete Applied Mathematics
Semi-preemptive routing on trees
Discrete Applied Mathematics
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The problem of routing a robot (or vehicle) between n stations in the plane in order to transport objects is well studied, even if the stations are specially arranged, e.g. on a linear track or circle. The robot may use either all or none of the stations for reloading. We will generalize these concepts of preemptiveness/nonpreemptiveness and allow the robot to choose k@?n reload-stations. We will show that the problem on the linear and circular track remains polynomially solvable.