Related papers: Minimizing Flow-Time on Unrelated Machines
We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
We consider the online problem of minimizing weighted flow-time on unrelated machines. Although much is known about this problem in the resource-augmentation setting, these results assume that jobs can be preempted. We give the first…
This paper considers the online machine minimization problem, a basic real time scheduling problem. The setting for this problem consists of n jobs that arrive over time, where each job has a deadline by which it must be completed. The goal…
A prominent problem in scheduling theory is the weighted flow time problem on one machine. We are given a machine and a set of jobs, each of them characterized by a processing time, a release time, and a weight. The goal is to find 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 problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For…
We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(\log P)$-competitive algorithm, where $P$ is the…
In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…
We consider the problem of scheduling $n$ jobs to minimize the makespan on $m$ unrelated machines, where job $j$ requires time $p_{ij}$ if processed on machine $i$. A classic algorithm of Lenstra et al. yields the best known approximation…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
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…
In this paper, we study the following batch scheduling model: find a schedule that minimizes total flow time for $n$ uniform length jobs, with release times and deadlines, where the machine is only actively processing jobs in at most $k$…
In the classical interval scheduling type of problems, a set of $n$ jobs, characterized by their start and end time, need to be executed by a set of machines, under various constraints. In this paper we study a new variant in which the jobs…
We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC '01, SODA '03, FOCS '18) all require exact knowledge of the processing time of each…
In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…
A very well-known machine model in scheduling allows the machines to be unrelated, modelling jobs that might have different characteristics on each machine. Due to its generality, many optimization problems of this form are very difficult…
We consider the problem of scheduling multiprocessor jobs to minimize the total completion time under the given energy budget. Each multiprocessor job requires more than one processor at the same moment of time. Processors may operate at…
This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are $n$ jobs and each job $j$ is associated with a…
Scheduling a set of jobs over a collection of machines is a fundamental problem that needs to be solved millions of times a day in various computing platforms: in operating systems, in large data clusters, and in data centers. Along with…