Metrical task systems on trees via mirror descent and unfair gluing
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 wellknown HST embedding theorems, this also gives an $O((\log n)^2)$competitive randomized algorithm for every $n$point metric space.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.04404
 Bibcode:
 2018arXiv180704404B
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Mathematics  Metric Geometry