Craig A. Tovey

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Recently, auction methods have been investigated as effective, decentralized methods for multi-robot coordination. Experimental research has shown great potential, but has not been complemented yet by theoretical analysis. In this paper we contribute a theoretical analysis of the performance of auction methods for multi-robot routing. We suggest a generic(More)
Cook [l] has shown that 3-SAT, the Boolean satisfiability problem restricted to instances with exactly three variables per clause, is NP-complete. This is a tightest possible restriction on the number of variables in a clause because as Even et al. [2] demonstrate, 2-SAT is in P. Horowitz and Sahni [5] point up the importance of finding the strongest(More)
This paper describes a predicate calculus in which graph problems can be expressed. Any problem possessing such an expression can be solved in linear time on any recursively constructed graph, once its decomposition tree is known. Moreover, the linear-time algorithm can be generatedautomatically from the expression, because all our theorems are proved(More)
Teams of robots are more fault tolerant than single robots, and auctions appear to be promising means for coordinating them. In a recent paper at “Robotics: Science and Systems 2005,” we analyzed a coordination system based on sequential single-item auctions. We showed that the coordination system is simple to implement and computation and communication(More)
Robotics researchers have used auction-based coordination systems for robot teams because of their robustness and efficiency. However, there is no research into systematic methods for deriving appropriate bidding rules for given team objectives. In this paper, we propose the first such method and demonstrate it by deriving bidding rules for three possible(More)
We recently noticed an error in our paper, “Local optimization on graphs”, which appeared in volume 23, 1989, pages 157-178, of Discrete Applied Mathematics. The error is not too serious, in that all of the lemmata, propositions, and theorems are correct as given. However, the divide-and-conquer algorithm in Section 2.1, p. 159, is incomplete. The necessary(More)
We study auction-like algorithms for the distributed allocation of tasks to cooperating agents. To reduce the team cost of sequential single-item auction algorithms, we generalize them to assign more than one additional task during each round, which increases their similarity to combinatorial auction algorithms. We show that, for a given number of(More)
We study pursuit-evasion problems where a number of pursuers have to clear a given graph. We study when polynomial-time algorithms exist to determine howmany pursuers are needed to clear a given graph and how a given number of pursuers should move on the graph to clear it with either a minimum sum of their travel distances or minimum task-completion time.(More)