In this paper, we consider the problem of tasking large numbers of homogenous robots to move to a set of specified goal locations, addressing both the assignment and trajectory planning subproblems concurrently. This is related to the standard linear Euclidean assignment problem except that the solution to the trajectory generation subproblem must result in timeparameterized trajectories and guarantee collision avoidance. We begin with a centralized approach and derive an optimal centralized

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... ution and study the computational complexity. The main contribution of this paper, however, is a decentralized algorithm with limited communication between neighbors that guarantees collision-avoidance and overcomes the computational challenges of the centralized method at the cost of suboptimal solutions. We demonstrate the performance of the algorithm as the number of robots is increased to tens of robots and the resulting increase in communication across neighbors required for safe execution.