Related papers: A Polylogarithmic-Competitive Algorithm for the k-…
We study three classical online problems -- $k$-server, $k$-taxi, and chasing size $k$ sets -- through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between…
The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. This paper introduces the marking algorithm, a simple randomized on-line algorithm for the paging problem, and…
We propose a $O(\log k \log n)$-competitive randomized algorithm for online node-weighted Steiner forest. This is essentially optimal and significantly improves over the previous bound of $O(\log^2 k \log n)$ by Hajiaghayi et al. [2017]. In…
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 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…
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…
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…
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…
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 study the problem of metrical service systems with multiple servers (MSSMS), which generalizes two well-known problems -- the $k$-server problem, and metrical service systems. The MSSMS problem is to service requests, each of which is an…
We consider the k-server problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size {\Omega}(n) is required to obtain a 1-competitive algorithm for sequences of size…
In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The…
We are given a set $P$ of $n$ points in the plane, and a sequence of axis-aligned squares that arrive in an online fashion. The online hitting set problem consists of maintaining, by adding new points if necessary, a set $H\subseteq P$ that…
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…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
We consider the generalized $k$-server problem on uniform metrics. We study the power of memoryless algorithms and show tight bounds of $\Theta(k!)$ on their competitive ratio. In particular we show that the \textit{Harmonic Algorithm}…
In the online metric bipartite matching problem, we are given a set $S$ of server locations in a metric space. Requests arrive one at a time, and on its arrival, we need to immediately and irrevocably match it to a server at a cost which is…
We show that the RandomCoordinateCut algorithm gives the optimal competitive ratio for explainable k-medians in l1. The problem of explainable k-medians was introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian in 2020. Several groups…
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…
Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called \textit{min-max} paging, where the objective is to minimize the maximum number of faults on any page. While…