Some voting schemes that are in principle susceptible to control are nevertheless resistant in practice due to excessive computational costs; others are vulnerable. We illustrate this in detail for plurality voting and for Condorcet voting.
— 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)
3-SAT is NP-complete when restricted to instances where each variable appears in at most four clauses. When no variable appears in more than three clauses, 3-SAT is trivial and SAT is NP-complete. When no variable appears in more than two clauses, SAT may be solved in linear time.
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)
We recently noticed an error in our paper, " Local optimization on graphs " , 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 changes are as follows (all changes are to p. 159): (2) In Steps 1 and 2, " S "… (More)
Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to ≈ 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along… (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 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)