Ramsey-type theorems for metric spaces with applications to online problems
<|reference_start|>Ramsey-type theorems for metric spaces with applications to online problems: A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively studied k-server problem. The proof is based on Ramsey-type theorems for metric spaces, that state that every metric space contains a large subspace which is approximately a hierarchically well-separated tree (and in particular an ultrametric). These Ramsey-type theorems may be of independent interest.<|reference_end|>
@article{bartal2004ramsey-type,
    title={Ramsey-type theorems for metric spaces with applications to online
  problems},
    author={Yair Bartal, Bela Bollobas, Manor Mendel},
    journal={J. Comput. System Sci. 72(5):890-921, 2006},
    year={2004},
    doi={10.1016/j.jcss.2005.05.008},
    archivePrefix={arXiv},
    eprint={cs/0406028},
    primaryClass={cs.DS}
}