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In this article, we consider a multi-agent path planning problem in a partially impeded environment. The impeded environment is represented by a graph with select road segments (edges) in disrepair impeding vehicular movement in the road…
Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…
We study the problem of distributed coverage control in a network of mobile agents arranged on a line. The goal is to design distributed dynamics for the agents to achieve optimal coverage positions with respect to a scalar density field…
Let $P$ be a set of points in the plane and let $m$ be an integer. The goal of Max Cover by Unit Disks problem is to place $m$ unit disks whose union covers the maximum number of points from~$P$. We are interested in the dynamic version of…
We investigate two fundamental problems in mobile computing: exploration and rendezvous, with two distinct mobile agents in an unknown graph. The agents may communicate by reading and writing information on whiteboards that are located at…
This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation,…
We consider the optimal multi-agent persistent monitoring problem defined by a team of cooperating agents visiting a set of nodes (targets) on a graph with the objective of minimizing a measure of overall node state uncertainty. The…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
In the facility location problem, the task is to place one or more facilities so as to minimize the sum of the agent costs for accessing their nearest facility. Heretofore, in the strategic version, agent locations have been assumed to be…
The study of counting point-hyperplane incidences in the $d$-dimensional space was initiated in the 1990's by Chazelle and became one of the central problems in discrete geometry. It has interesting connections to many other topics, such as…
A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Given a point set P in 2D, the problem of finding the smallest set of unit disks that cover all of P is NP-hard. We present a simple algorithm for this problem with an approximation factor of 25/6 in the Euclidean norm and 2 in the max…
In this paper, we investigate the $k$-Facility Location Problem ($k$-FLP) within the Bayesian Mechanism Design framework, in which agents' preferences are samples of a probability distributed on a line. Our primary contribution is…
This paper considers a network of agents, where each agent is assumed to take actions optimally with respect to a predefined payoff function involving the latest actions of the agent's neighbors. Neighborhood relationships stem from payoff…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
Given a set of $m$ agents and a set of $n$ items, where agent $A$ has utility $u_{A,i}$ for item $i$, our goal is to allocate items to agents to maximize fairness. Specifically, the utility of an agent is the sum of its utilities for items…
We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…
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…