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We present an $O((\log k)^2)$-competitive randomized algorithm for the $k$-server problem on hierarchically separated trees (HSTs).
Problem Complexity and Method Efficiency in Optimization
A. Nemirovski and D. Yudin · 1983
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Differential Inclusions: Set-Valued Maps and Viability Theory
Jean Pierre Aubin and A. Cellina · 1984
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Competitive algorithms for server problems
Mark S. Manasse, Lyle A. McGeoch, and Daniel D. Sleator · 1990
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Competitive paging algorithms
A. Fiat, R. M. Karp, M. Luby, L. A. McGeoch, D. D. Sleator, and Young N. E · 1991
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A strongly competitive randomized paging algorithm
Lyle A. McGeoch and Daniel D. Sleator · 1991
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Convex analysis and minimization algorithms, Volume I: Fundamentals
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 1993
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On the k k -server conjecture
Elias Koutsoupias and Christos H. Papadimitriou · 1995
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Probabilistic approximations of metric spaces and its algorithmic applications
Yair Bartal · 1996
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On approximating arbitrary metrices by tree metrics
Yair Bartal · 1998
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Allan Borodin and Ran El-Yaniv · 1998
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Finely-competitive paging
Avrim Blum, Carl Burch, and Adam Kalai · 1999
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A tight bound on approximating arbitrary metrics by tree metrics
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Yair Bartal, Nathan Linial, Manor Mendel, and Assaf Naor · 2005
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Ramsey-type theorems for metric spaces with applications to online problems
Yair Bartal, Béla Bollobás, and Manor Mendel · 2006
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The k k -server problem
Elias Koutsoupias · 2009
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A primal-dual randomized algorithm for weighted paging
Nikhil Bansal, Niv Buchbinder, and Joseph Naor · 2012
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A regularization approach to metrical task systems
Jacob Abernethy, Peter Bartlett, Niv Buchbinder, and Isabelle Stanton · 2014
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Competitive analysis via regularization
Niv Buchbinder, Shahar Chen, and Joseph (Seffi) Naor · 2014
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A polylogarithmic-competitive algorithm for the k k -server problem
Nikhil Bansal, Niv Buchbinder, Aleksander Madry, and Joseph Naor · 2015
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Convex optimization: Algorithms and complexity
Sébastien Bubeck · 2015
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Randomized k k -server on hierarchical binary trees
Aaron Coté, Adam Meyerson, and Laura Poplawski · 2008
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Introduction to online convex optimization
Elad Hazan · 2016
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