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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 extend the Mobile Server Problem, introduced in SPAA'17, to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. In order to reduce communication costs, the positions…
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…
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,…
We study deterministic online algorithms for the problem of chasing sets of cardinality at most $k$ in a metric space, also known as metrical service systems and equivalent to width-$k$ layered graph traversal. We resolve the 30-year-old…
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…
For any given metric space, obtaining an offline optimal solution to the classical $k$-server problem can be reduced to solving a minimum-cost partial bipartite matching between two point sets $A$ and $B$ within that metric space. For…
We consider a generalization of the fundamental online metrical service systems (MSS) problem where the feasible region can be transformed between requests. In this problem, which we call T-MSS, an algorithm maintains a point in a metric…
Motivated by Internet targeted advertising, we address several ad allocation problems. Prior work has established these problems admit no randomized online algorithm better than $(1-\frac{1}{e})$-competitive…
We consider a variant of the online buffer management problem in network switches, called the $k$-frame throughput maximization problem ($k$-FTM). This problem models the situation where a large frame is fragmented into $k$ packets and…
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 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 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 a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending…
The k-forest problem is a common generalization of both the k-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices $V$, with $m$ demand pairs $\subseteq V \times V$ and a ``target'' $k\le m$, the goal is…
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…
In collective tree exploration, a team of $k$ mobile agents is tasked to go through all edges of an unknown tree as fast as possible. An edge of the tree is revealed to the team when one agent becomes adjacent to that edge. The agents start…
In the $k$-connected directed Steiner tree problem ($k$-DST), we are given an $n$-vertex directed graph $G=(V,E)$ with edge costs, a connectivity requirement $k$, a root $r\in V$ and a set of terminals $T\subseteq V$. The goal is to find a…
We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…