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The pinwheel problem is a real-time scheduling problem that asks, given $n$ tasks with periods $a_i \in \mathbb{N}$, whether it is possible to infinitely schedule the tasks, one per time unit, such that every task $i$ is scheduled in every…

Pinwheel Scheduling aims to find a perpetual schedule for unit-length tasks on a single machine subject to given maximal time spans (a.k.a. frequencies) between any two consecutive executions of the same task. The density of a Pinwheel…

The density bound for schedulability for general pinwheel instances is $\frac{5}{6}$, but density bounds better than $\frac{5}{6}$ can be shown for cases in which the minimum element $m$ of the instance is large. Several recent works have…

For a sequence of tasks, each with a positive integer period, the pinwheel scheduling problem involves finding a valid schedule in the sense that the schedule performs one task per day and each task is performed at least once every…

Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…

A classical multi-agent fence patrolling problem asks: What is the maximum length $L$ of a line that $k$ agents with maximum speeds $v_1,\ldots,v_k$ can patrol if each point on the line needs to be visited at least once every unit of time.…

The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…

Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…

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…

In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time between consecutive occurrences of the same edge. This NP-hard…

We push the limit in planning collision-free motions for routing uniform labeled discs in two dimensions. First, from a theoretical perspective, we show that the constant-factor time-optimal routing of labeled discs can be achieved using a…

Time-dependent scheduling with linear deterioration involves determining when to execute jobs whose processing times degrade as their beginning is delayed. Each job i is associated with a release time r_i and a processing time function…

This paper addresses the sweep coverage problem of multi-agent systems in uncertain regions. A new formulation of distributed sweep coverage is proposed to cooperatively complete the workload in the uncertain region. Specifically, each…

We develop a hybrid system model to describe the behavior of multiple agents cooperatively solving an optimal coverage problem under energy depletion and repletion constraints. The model captures the controlled switching of agents between…

The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism…

In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…

In this paper, we study the active time scheduling problem. We are given n jobs with integral processing times each of which has an integral release time and deadline. The goal is to schedule all the jobs on a machine that can work on b…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers, where the aim is that of maximizing the throughput. Each node in the network has a local buffer of bounded size…

Pinwheel Scheduling is a fundamental scheduling problem, in which each task $i$ is associated with a positive integer $d_i$, and the objective is to schedule one task per time slot, ensuring each task perpetually appears at least once in…