We consider the problem of allocating a number of exploration tasks to a team of mobile robots. Each task consists of a target location that needs to be visited by a robot. The objective of the allocation is to minimize the total cost, that is, the sum of the travel costs of all robots for visiting all targets. We show that finding an optimal allocation is an NP-hard problem, even in known environments. The main contribution of this paper is PRIM ALLOCATION, a simple and fast approximate algorithm for allocating targets to robots which provably computes allocations whose total cost is at most twice as large as the optimal total cost. We then cast PRIM ALLOCATION in terms of a multi-round single-item auction where robots bid on targets, which allow for a decentralized implementation. To the best of our knowledge, PRIM ALLOCATION is the first auction-based allocation algorithm that provides a guarantee on the quality of its allocations. Our experimental results in a multi-robot simulator demonstrate that PRIM ALLOCATION is fast and results in close-to-optimal allocations despite its simplicity and decentralized nature. In particular, it needs an order of magnitude fewer bids than a computationally intensive allocation algorithm based on combinatorial auctions, yet its allocations are at least as good.

We study how to coordinate a team of mobile robots to visit a number of given targets in a partially unknown terrain. Robotics researchers have studied single-item auctions to perform this exploration task but these do not make synergies between the targets into account. We therefore design combinatorial auctions, propose different combinatorial bidding strategies and compare their performance with each other, as well as to single item auctions and an optimal centralized mechanism. Our computational results in teambots, a multi-robot simulator, indicate that combinatorial auctions generally lead to significantly superior team performance than single-item auctions, and generate very good results compared to an optimal centralized mechanism.

We consider a very general online scheduling problem with an objective to minimize the maximum level of resource allocated. We find a simple characterization of an optimal deterministic online algorithm. We develop further results for the two, more specific problems of single resource scheduling and hierarchical line balancing. We determine how to compute optimal online algorithms for both problems using linear programming and integer programming, respectively. We show that randomized algorithms can outperform deterministic algorithms, but only if the amount of work done is a nonconcave function of resource allocation.