k-server via multiscale entropic regularization
Name
1711.01085.pdf
Description
Submitted version
Size
308.08 KB
Format
Adobe PDF
Checksum (MD5)
3dcbfc6737d5118f0b3133a5d32965ca
Author(s)
Bubeck, Sébastien
Cohen, Michael B.
Lee, Yin Tat
Lee, James R.
Mądry, Aleksander
Date Issued
June 2018
Publisher
Association for Computing Machinery (ACM)
Citation
Bubeck, Sébastien, Cohen, Michael B., Lee, Yin Tat, Lee, James R. and Mądry, Aleksander. 2018. "k-server via multiscale entropic regularization."
Version
Original manuscript
Abstract
© 2018 Copyright held by the owner/author(s). We present an O((log k)2)-competitive randomized algorithm for the k-server problem on hierarchically separated trees (HSTs). This is the first o(k)-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with Bartal’s static HST embedding reduction, this leads to an O((log k)2 log n)-competitive algorithm on any n-point metric space. We give a new dynamic HST embedding that yields an O((log k)3 log ∆)-competitive algorithm on any metric space where the ratio of the largest to smallest non-zero distance is at most ∆.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/3188745.3188798
