Related papers: Randomized $k$-server in polynomial time
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 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…
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…
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 time-optimal $k$-server problem minimizes the time spent serving all requests instead of the distances traveled. We give a lower bound of $2k-1$ on the competitive ratio of any deterministic online algorithm for this problem, which…
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 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 study the weighted $k$-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) $k$-server problem which has a polynomial-time…
We consider online algorithms for the $k$-server problem on trees of size $n$. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, the existing implementations have…
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…
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server $s_i$ lies in its own metric space $M_i$. A request is a k-tuple $r = (r_1,r_2,\dotsc,r_k)$ and to serve it,…
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 study a variant of the $k$-server problem, the infinite server problem, in which infinitely many servers reside initially at a particular point of the metric space and serve a sequence of requests. In the framework of competitive…
The weighted $k$-server problem is a natural generalization of the $k$-server problem in which the cost incurred in moving a server is the distance traveled times the weight of the server. Even after almost three decades since the seminal…
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…
In this paper, we study a stochastic variant of the celebrated k-server problem. In the k-server problem, we are required to minimize the total movement of k servers that are serving an online sequence of t requests in a metric. In the…
In this paper we study a dynamic resource allocation problem which we call the stochastic k-server problem. In this problem, requests for some service to be performed appear at various locations over time, and we have a collection of k…
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 how to restrict the analysis of a class of online problems that includes the $k$-server problem in finite metrics such that we only have to consider finite sequences of request. When applying the restrictions, both the optimal…
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…