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arXiv · 1807.04404

Metrical task systems on trees via mirror descent and unfair gluing

Sébastien Bubeck·Michael B. Cohen·James R. Lee·Yin Tat Lee
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Abstract

We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem. For the special case of hierarchically separated trees (HSTs), we use mirror descent to refine the standard approach based on gluing unfair metrical task systems. This yields an $O(\log n)$-competitive algorithm for HSTs, thus removing an extraneous $\log\log n$ in the bound of Fiat and Mendel (2003). Combined with well-known HST embedding theorems, this also gives an $O((\log n)^2)$-competitive randomized algorithm for every $n$-point metric space.

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Sébastien Bubeck, Michael B. Cohen, James R. Lee, Yin Tat Lee. 2018-07-12. Metrical task systems on trees via mirror descent and unfair gluing. https://arxiv.org/abs/1807.04404

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