Related papers: The $(1|1)_R$-Centroid Problem on the Plane
Electricity cost is a dominant and rapidly growing expense in data centers. Unfortunately, much of the consumed energy is wasted because servers are idle for extended periods of time. We study a capacity management problem that dynamically…
We study the online problem of assigning a moving point to a base-station region that contains it. For instance, the moving object could represent a cellular phone and the base station could represent the coverage zones of cell towers. Our…
We consider a bichromatic two-center problem for pairs of points. Given a set $S$ of $n$ pairs of points in the plane, for every pair, we want to assign a red color to one point and a blue color to the other, in such a way that the value…
In this article, we consider the $c$-dispersion problem in a metric space $(X,d)$. Let $P=\{p_{1}, p_{2}, \ldots, p_{n}\}$ be a set of $n$ points in a metric space $(X,d)$. For each point $p \in P$ and $S \subseteq P$, we define…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. The previous best…
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…
We consider $n$ unit-speed mobile agents initially positioned at the center of a unit disk, tasked with inspecting all points on the disk's perimeter. A perimeter point is considered covered if an agent located outside the disk's interior…
In the {\em Movement Repairmen (MR)} problem we are given a metric space $(V, d)$ along with a set $R$ of $k$ repairmen $r_1, r_2, ..., r_k$ with their start depots $s_1, s_2, ..., s_k \in V$ and speeds $v_1, v_2, ..., v_k \geq 0$…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
Fast shipping and efficient routing are key problems of modern logistics. Building on previous studies that address package delivery from a source node to a destination within a graph using multiple agents (such as vehicles, drones, and…
Given two point sets S and T, we study the many-to-many matching with demands problem (MMD problem) which is a generalization of the many-to-many matching problem (MM problem). In an MMD, each point of one set must be matched to a given…
Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in…
We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here $n$ is the number of nodes in the…
In the chasing convex bodies problem, an online player receives a request sequence of $N$ convex sets $K_1,\dots, K_N$ contained in a normed space $\mathbb R^d$. The player starts at $x_0\in \mathbb R^d$, and after observing each $K_n$…
The Team Orienteering Problem (TOP) is an attractive variant of the Vehicle Routing Problem (VRP). The aim is to select customers and at the same time organize the visits for a vehicle fleet so as to maximize the collected profits and…
The dispersion problem has been widely studied in computational geometry and facility location, and is closely related to the packing problem. The goal is to locate n points (e.g., facilities or persons) in a k-dimensional polytope, so that…
In the online non-metric variant of the facility location problem, there is a given graph consisting of a set $F$ of facilities (each with a certain opening cost), a set $C$ of potential clients, and weighted connections between them. The…
In this paper we study the classical problem of throughput maximization. In this problem we have a collection $J$ of $n$ jobs, each having a release time $r_j$, deadline $d_j$, and processing time $p_j$. They have to be scheduled…