A polylog(n)-competitive algorithm for metrical task systems

@inproceedings{Bartal1997APA,
  title={A polylog(n)-competitive algorithm for metrical task systems},
  author={Yair Bartal and Avrim Blum and Carl Burch and Andrew Tomkins},
  booktitle={Symposium on the Theory of Computing},
  year={1997}
}
We present a randomized on-line algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against an oblivious adversary. This is the first algorithm to achieve a sublinear competitive ratio for all metric spaces. Our algorit hm uses a recent result of Bartal [Bar96] that an arbitrary metr ic space can be probabilistically approximated by a set of metric spaces called “ k-hierarchical well-separated trees” ( kHST’s). Indeed, the… 

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