Related papers: Approximation results for makespan minimization wi…
We consider the following special case of minimizing makespan. A set of jobs $J$ and a set of machines $M$ are given. Each job $j \in J$ can be scheduled on a machine from a subset $M_j$ of $M$. The processing time of $j$ is the same on all…
We consider online scheduling on multiple machines for jobs arriving one-by-one with the objective of minimizing the makespan. For any number of identical parallel or uniformly related machines, we provide a competitive-ratio approximation…
We consider the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities where each job can only be processed on a specified subset of machines called its processing set. For the case of…
We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant…
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…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
We study problems of scheduling jobs on related machines so as to minimize the makespan in the setting where machines are strategic agents. In this problem, each job $j$ has a length $l_{j}$ and each machine $i$ has a private speed $t_{i}$.…
This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs…
We consider the classical makespan minimization scheduling problem where $n$ jobs must be scheduled on $m$ identical machines. Using weighted random sampling, we developed two sublinear time approximation schemes: one for the case where $n$…
Given $n$ jobs with processing times $p_1,\dotsc,p_n\in\mathbb N$ and $m\le n$ machines with speeds $s_1,\dotsc,s_m\in\mathbb N$ our goal is to allocate the jobs to machines minimizing the makespan. We present an algorithm that solves the…
We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of $2$ and $\min\{m-k+1,…
Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be…
The parallel machine scheduling problem has been a popular topic for many years due to its theoretical and practical importance. This paper addresses the robust makespan optimization problem on unrelated parallel machine scheduling with…
We consider the classic problem of scheduling jobs on unrelated machines so as to minimize the weighted sum of completion times. Recently, for a small constant $\varepsilon >0 $, Bansal et al. gave a $(3/2-\varepsilon)$-approximation…
We present a unified framework for designing deterministic monotone polynomial time approximation schemes (PTAS's) for a wide class of scheduling problems on uniformly related machines. This class includes (among others) minimizing the…
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the…
We consider non-preemptive scheduling problems on parallel identical machines where machines change their status from being available to being unavailable and vice versa along the time horizon. The particular form of unavailability we…
The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is…
We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is…