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We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with…
The goal of this paper is to develop a numerical algorithm that solves a two-dimensional elliptic partial differential equation in a polygonal domain using tensor methods and ideas from isogeometric analysis. The proposed algorithm is based…
This paper addresses a synchronization problem that arises when a team of aerial robots (ARs) need to communicate while performing assigned tasks in a cooperative scenario. Each robot has a limited communication range and flies within a…
The \emph{Tree Augmentation Problem (TAP)} is given a tree $T=(V,E_T)$ and additional set of {\em links} $E$ on $V\times V$, find $F \subseteq E$ such that $T \cup F$ is $2$-edge-connected, and $|F|$ is minimum. The problem is APX-hard…
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
General-purpose robots require diverse repertoires of behaviors to complete challenging tasks in real-world unstructured environments. To address this issue, goal-conditioned reinforcement learning aims to acquire policies that can reach…
A challenge in robot grasping is to achieve task-grasping which is to select a grasp that is advantageous to the success of tasks before and after grasps. One of the frameworks to address this difficulty is Learning-from-Observation (LfO),…
For legged robots to operate in complex terrains, they must be robust to the disturbances and uncertainties they encounter. This paper contributes to enhancing robustness through the design of fall detection/prediction algorithms that will…
In this paper, we study the problem of coverage planning by a mobile robot with a limited energy budget. The objective of the robot is to cover every point in the environment while minimizing the traveled path length. The environment is…
We study the problem of assigning robots with actions to track targets. The objective is to optimize the robot team's tracking quality which can be defined as the reduction in the uncertainty of the targets' states. Specifically, we…
Multi-robot systems are uniquely well-suited to performing complex tasks such as patrolling and tracking, information gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A…
Two cooperating, autonomous mobile robots with arbitrary nonzero max speeds are placed at arbitrary initial positions in the plane. A remotely detonated bomb is discovered at some source location and must be moved to a safe distance away…
We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…
This paper presents an approach to externally influencing a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. To this end, a continuous-time…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…