Related papers: Towards the k-server conjecture: A unifying potent…
The deterministic $k$-server conjecture states that there is a $k$-competitive deterministic algorithm for the $k$-server problem for any metric space. We show that the work function algorithm is $3$-competitive for the $3$-server problem…
The Work Function Algorithm is the most effective deterministic on-line algorithm for the k-server problem. Koutsoupias and Papadimitriou proved WFA is (2k-1) competitive. However the best known implementation of WFA requires time O(i^2) to…
We introduce a code-based challenge for automated, open-ended mathematical discovery based on the $k$-server conjecture, a central open problem in competitive analysis. The task is to discover a potential function satisfying a large…
We initiate a formal study of fairness for the $k$-server problem, where the objective is not only to minimize the total movement cost, but also to distribute the cost equitably among servers. We first define a general notion of…
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 $k$-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively for decades. We present a model generalizing the $k$-Server Problem by preferences of the requests, where the…
The weighted $k$-server problem is a natural generalization of the $k$-server problem where each server has a different weight. We consider the problem on uniform metrics, which corresponds to a natural generalization of paging. Our main…
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,…
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…
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…
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 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 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…
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 study the fundamental online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request sequence, we assume that there is given some advice (e.g.…
This paper presents a mistake in work function algorithm of k-server conjecture. That is, the monotonicity of the work function is not always true.
The generalized 2-server problem is an online optimization problem where a sequence of requests has to be served at minimal cost. Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the…
The problem of online scheduling of multi-server jobs is considered, where there are a total of $K$ servers, and each job requires concurrent service from multiple servers for it to be processed. Each job on its arrival reveals its…
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 $k$-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…