Related papers: Approximation Algorithms for Union and Intersectio…
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…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
A set-family ${\cal F}$ is disjointness-compliable if $A' \subseteq A \in {\cal F}$ implies $A' \in {\cal F}$ or $A \setminus A' \in {\cal F}$; if ${\cal F}$ is also symmetric then ${\cal F}$ is proper. A classic result of Goemans and…
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…
Arkin et al.~\cite{ArkinBCCJKMM17} recently introduced \textit{partitioned pairs} network optimization problems: given a metric-weighted graph on $n$ pairs of nodes, the task is to color one node from each pair red and the other blue, and…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
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…
We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical…
We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points $P$ in the plane, together with a subset of pairs of points in $P$ (which we call demands), find a minimum-cardinality superset of…
The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Given a graph G, the {\em maximum internal spanning tree problem} (MIST for short) asks for computing a spanning tree T of G such that the number of internal vertices in T is maximized. MIST has possible applications in the design of…
In traditional massive content distribution with multiple sessions, the sessions form separate overlay networks and operate independently, where some sessions may suffer from insufficient resources even though other sessions have excessive…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
We study problems related to connecting multi-interface networks of wireless devices. These problems are modeled using graphs, where vertices represent the devices and edges represent potential communication links. Each vertex can activate…
Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…