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The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…
In this paper we initiate the study of the heterogeneous capacitated $k$-center problem: given a metric space $X = (F \cup C, d)$, and a collection of capacities. The goal is to open each capacity at a unique facility location in $F$, and…
Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that…
We study the following range searching problem: Preprocess a set $P$ of $n$ points in the plane with respect to a set $\mathcal{O}$ of $k$ orientations % , for a constant, in the plane so that given an $\mathcal{O}$-oriented convex polygon…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
This paper addresses two problems lying at the intersection of geometric analysis and theoretical computer science: The non-linear isomorphic Dvoretzky theorem and the design of good approximate distance oracles for large distortion. We…
In the Edge-Disjoint Paths with Congestion problem (EDPwC), we are given an undirected n-vertex graph G, a collection M={(s_1,t_1),...,(s_k,t_k)} of demand pairs and an integer c. The goal is to connect the maximum possible number of the…
We consider the {\em matroid median} problem \cite{KrishnaswamyKNSS11}, wherein we are given a set of facilities with opening costs and a matroid on the facility-set, and clients with demands and connection costs, and we seek to open an…
Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…
Given a set of points $P$ and axis-aligned rectangles $\mathcal{R}$ in the plane, a point $p \in P$ is called \emph{exposed} if it lies outside all rectangles in $\mathcal{R}$. In the \emph{max-exposure problem}, given an integer parameter…
In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances…
In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not…
We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of…
Given a set $P$ of $n$ weighted points and a set $S$ of $m$ disks in the plane, the hitting set problem is to compute a subset $P'$ of points of $P$ such that each disk contains at least one point of $P'$ and the total weight of all points…
Fairness considerations have motivated new clustering problems and algorithms in recent years. In this paper we consider the Priority Matroid Median problem which generalizes the Priority $k$-Median problem that has recently been studied.…
We give the first polylogarithmic-competitive randomized online algorithm for the $k$-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of O(log^3 n log^2 k log log n) for any…
We study the maximum set coverage problem in the massively parallel model. In this setting, $m$ sets that are subsets of a universe of $n$ elements are distributed among $m$ machines. In each round, these machines can communicate with each…
We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do…
We consider the basic problem of learning an unknown partition of $n$ elements into at most $k$ sets using simple queries that reveal information about a small subset of elements. Our starting point is the well-studied pairwise same-set…