Related papers: Freeze-Tag in $L_1$ has Wake-up Time Five
Speed-robust scheduling is the following two-stage problem of scheduling $n$ jobs on $m$ uniformly related machines. In the first stage, the algorithm receives the value of $m$ and the processing times of $n$ jobs; it has to partition the…
The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model. We given an alternate and elementary…
Robots are becoming an increasingly common part of scientific work within laboratory environments. In this paper, we investigate the problem of designing \emph{schedules} for completing a set of tasks at fixed locations with multiple robots…
We consider n robots with limited visibility: each robot can observe other robots only up to a constant distance denoted as the viewing range. The robots operate in discrete rounds that are either fully synchronous (FSync) or…
We consider several problems relating to strongly-connected directed networks of identical finite-state processors that work synchronously in discrete time steps. The conceptually simplest of these is the Wake Up and Report Problem; this is…
In a rendezvous task, some mobile agents dispersed in a network have to gather at an arbitrary common site. We consider the rendezvous problem on the infinite labeled line, with $2$ agents, without communication, and a synchronous notion of…
We propose an approach to find low-makespan solutions to multi-robot multi-task planning problems in environments where robots block each other from completing tasks simultaneously. We introduce a formulation of the problem that allows for…
We introduce and study a new problem concerning the exploration of a geometric domain by mobile robots. Consider a line segment $[0,I]$ and a set of $n$ mobile robots $r_1,r_2,..., r_n$ placed at one of its endpoints. Each robot has a {\em…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
We study unlabeled multi-robot motion planning for unit-disk robots in a polygonal environment. Although the problem is hard in general, polynomial-time solutions exist under appropriate separation assumptions on start and target positions.…
Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollob\'as in 1968. In this process, we start with initial "infected" set of edges $E_0$, and we infect new edges according to a predetermined rule. Given a graph…
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. This problem is…
We consider the minimum makespan problem for $n$ tasks and two unrelated parallel selfish machines. Let $R_n$ be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms…
In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model.…
We consider the unlabeled motion-planning problem of $m$ unit-disc robots moving in a simple polygonal workspace of $n$ edges. The goal is to find a motion plan that moves the robots to a given set of $m$ target positions. For the unlabeled…
We study envy-free mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envy-free poly-time mechanism that approximates the minimal makespan to…
We consider a 1-machine scheduling problem where the temperature of a job rises during processing, and cools down when not being processed according to given linear heating and cooling rates. No job's temperature is allowed to rise above a…
We study the wake-up problem in distributed networks, where an adversary awakens a subset of nodes at arbitrary times, and the goal is to wake up all other nodes as quickly as possible by sending only few messages. We prove the following…
Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound…
Cooperation between mobile robots and wireless sensor networks is a line of research that is currently attracting a lot of attention. In this context, we study the following problem of barrier coverage by stationary wireless sensors that…