Related papers: k-server via multiscale entropic regularization
We exhibit an $O((\log k)^6)$-competitive randomized algorithm for the $k$-server problem on any metric space. It is shown that a potential-based algorithm for the fractional $k$-server problem on hierarchically separated trees (HSTs) with…
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log…
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…
We give the first polylogarithmic-competitive randomized online algorithm for the $k$-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of O(log^3 n log^2 k log log n) for any…
We study the $k$-server problem in the resource augmentation setting i.e., when the performance of the online algorithm with $k$ servers is compared to the offline optimal solution with $h \leq k$ servers. The problem is very poorly…
We consider the $k$-server problem on trees and HSTs. We give an algorithm based on Bregman projections. This algorithm has a competitive ratios that match some of the recent results given by Bubeck et al. (STOC 2018), whose algorithm was…
We show that on every $n$-point HST metric, there is a randomized online algorithm for metrical task systems (MTS) that is $1$-competitive for service costs and $O(\log n)$-competitive for movement costs. In general, these refined…
We consider the online $k$-taxi problem, a generalization of the $k$-server problem, in which $k$ taxis serve a sequence of requests in a metric space. A request consists of two points $s$ and $t$, representing a passenger that wants to be…
We consider online algorithms for the $k$-server problem on trees. There is a $k$-competitive algorithm for this problem, and it is the best competitive ratio. M. Chrobak and L. Larmore provided it. At the same time, the existing…
In this paper, we show that there is an O(log k log^2 n)-competitive randomized algorithm for the k-sever problem on any metric space with n points, which improved the previous best competitive ratio O(log^2 k log^3 n log log n) by Nikhil…
We study the resource augmented version of the $k$-server problem, also known as the $k$-server problem against weak adversaries or the $(h,k)$-server problem. In this setting, an online algorithm using $k$ servers is compared to an offline…
We study the design of computationally efficient randomized algorithms for the $k$-server problem. Existing randomized algorithms with the best known competitive ratios are, on the one hand, inherently implicit and, on the other hand,…
The generalized $k$-server problem is an extension of the weighted $k$-server problem, which in turn extends the classic $k$-server problem. In the generalized $k$-server problem, each of $k$ servers $s_1, \dots, s_k$ remains in its own…
A natural variant of the classical online $k$-server problem is the Weighted $k$-server problem, where the cost of moving a server is its weight times the distance through which it moves. Despite its apparent simplicity, the weighted…
In this paper, we settle the randomized $k$-sever conjecture for the following metric spaces: line, circle, Hierarchically well-separated tree (HST). Specially, we show that there are $O(\log k)$-competitive randomized $k$-sever algorithms…
We prove a few new lower bounds on the randomized competitive ratio for the $k$-server problem and other related problems, resolving some long-standing conjectures. In particular, for metrical task systems (MTS) we asympotically settle the…
The weighted $k$-server is a variant of the $k$-server problem, where the cost of moving a server is the server's weight times the distance through which it moves. The problem is famous for its intriguing properties and for evading standard…
We consider the online $k$-taxi problem, a generalization of the $k$-server problem, in which $k$ servers are located in a metric space. A sequence of requests is revealed one by one, where each request is a pair of two points, representing…
We develop a new approach for online network design and obtain improved competitive ratios for several problems. Our approach gives natural deterministic algorithms and simple analyses. At the heart of our work is a novel application of…
The weighted $k$-server problem is a generalization of the $k$-server problem in which the cost of moving a server of weight $\beta_i$ through a distance $d$ is $\beta_i\cdot d$. The weighted server problem on uniform spaces models caching…