Journal of the ACM (JACM)
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
Randomized robot navigation algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Better algorithms for unfair metrical task systems and applications
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A general decomposition theorem for the k-server problem
Information and Computation
A General Decomposition Theorem for the k-Server Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On metric ramsey-type phenomena
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight threshold for metric Ramsey phenomena
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Ramsey-type theorems for metric spaces with applications to online problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
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In this paper, the authors prove lower bounds on the competitive ratio of randomized algorithms for two on-line problems: the $k$-server problem, suggested by Manasse, McGeoch, and Sleator [Competitive algorithms for on-line problems, J. Algorithms, 11 (1990), pp. 208--230], and an on-line motion-planning problem due to Papadimitriou and Yannakakis [Shortest paths without a map, Lecture Notes in Comput. Sci. 372, Springer-Verlag, New York, 1989, pp. 610--620]. The authors prove, against an oblivious adversary, an $\Omega(\log k)$ lower bound on the competitive ratio of any randomized on-line $k$-server algorithm in any sufficiently large metric space, an $\Omega(\log\log k)$ lower bound on the competitive ratio of any randomized on-line $k$-server algorithm in any metric space with at least $k+1$ points, and an $\Omega(\log\log n)$ lower bound on the competitive ratio of any on-line motion-planning algorithm for a scene with $n$ obstacles. Previously, no superconstant lower bound on the competitive ratio of randomized on-line algorithms was known for any of these problems.