Related papers: Weighted Chairman Assignment and Flow-Time Schedul…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…
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…
This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with…
We study the approximability of two related machine scheduling problems. In the late work minimization problem, there are identical parallel machines and the jobs have a common due date. The objective is to minimize the late work, defined…
The open shop problem is to find a minimum makespan schedule to process each job $J_i$ on each machine $M_q$ for $p_{iq}$ time such that, at any time, each machine processes at most one job and each job is processed by at most one machine.…
In the Scheduling Machines with Capacity Constraints problem, we are given k identical machines, each of which can process at most m_i jobs. M jobs are also given, where job j has a non-negative processing time length t_j >= 0. The task is…
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_{\phi}-R^m_{\phi})g \\ \frac{\partial \phi}{\partial t} &=\frac{m}{2}(R^m_{\phi}-r^m_{\phi}) \end{array} \right. ~~\mbox{ in }M…
For a general adapted integrable right-continuous with left limits (RCLL) process $(X_t)_{t\in[0,\tau]}$ taking values in a metric space $(\mathcal E,d)$, we show (among other things) that for every $m\in(1,\infty)$ $$…
One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time p_{ij} if processed on…
This paper addresses the scheduling problem in mobile social networks. We begin by proving that the approximation ratio analysis presented in the paper by Zhang \textit{et al.} (IEEE Transactions on Mobile Computing, 2025) is incorrect, and…
We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…
We consider Johnson's rule for minimizing the makespan in the two-machine flow shop problem. Although its worst-case time complexity is O(n log n), we show that it is possible to detect in linear time whether a full sorting of jobs can be…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
This paper addresses the problem of scheduling jobs on identical machines with conflict constraints, where certain jobs cannot be scheduled simultaneously on different machines. We focus on the case where conflicts can be represented by a…
This paper studies the scheduling of jobs of different families on parallel machines with qualification constraints. Originating from semiconductor manufacturing, this constraint imposes a time threshold between the execution of two jobs of…
We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online \emph{non-clairvoyant} setting. In this problem, a set of jobs $J$ arrive over time to be scheduled on a set of $M$ machines.…
A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…
Datacenter networks commonly facilitate the transmission of data in distributed computing frameworks through coflows, which are collections of parallel flows associated with a common task. Most of the existing research has concentrated on…
We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion…
We aim to maximize the energy efficiency, gauged as average energy cost per job, in a large-scale server farm with various storage or/and computing components modeled as parallel abstracted servers. Each server operates in multiple power…