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We consider the $k$-server problem on trees and HSTs. We give an algorithmbased on Bregman projections. This algorithm has a competitive ratios thatmatch some of the recent results given by Bubeck et al. (STOC 2018), whosealgorithm was based on mirror-descent-based continuous dynamics prescribed viaa differential inclusion.

$k$-Servers with a Smile: Online Algorithms via Projections