Related papers: Memoryless Algorithms for the Generalized $k$-serv…
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.…
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…
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 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 give a memoryless scale-invariant randomized algorithm for the Buffer Management with Bounded Delay problem that is e/(e-1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
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…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
Machine learning algorithms are designed to make accurate predictions of the future based on existing data, while online algorithms seek to bound some performance measure (typically the competitive ratio) without knowledge of the future.…
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 study the $k$-server problem with time-windows. In this problem, each request $i$ arrives at some point $v_i$ of an $n$-point metric space at time $b_i$ and comes with a deadline $e_i$. One of the $k$ servers must be moved to $v_i$ at…
In this paper, we study the uniform capacitated $k$-median problem. Obtaining a constant approximation algorithm for this problem is a notorious open problem; most previous works gave constant approximations by either violating the capacity…
In submodular $k$-secretary problem, the goal is to select $k$ items in a randomly ordered input so as to maximize the expected value of a given monotone submodular function on the set of selected items. In this paper, we introduce a…
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 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 study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…
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 study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…
We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…
In the $k$-median problem, given a set of locations, the goal is to select a subset of at most $k$ centers so as to minimize the total cost of connecting each location to its nearest center. We study the uniform hard capacitated version of…