• Corpus ID: 16938238

# Online Algorithms for Machine Minimization

@article{Devanur2014OnlineAF,
title={Online Algorithms for Machine Minimization},
author={Nikhil R. Devanur and Konstantin Makarychev and Debmalya Panigrahi and Grigory Yaroslavtsev},
journal={ArXiv},
year={2014},
volume={abs/1403.0486}
}
• Published 3 March 2014
• Computer Science
• ArXiv
In this paper, we consider the online version of the machine minimization problem (introduced by Chuzhoy et al., FOCS 2004), where the goal is to schedule a set of jobs with release times, deadlines, and processing lengths on a minimum number of identical machines. Since the online problem has strong lower bounds if all the job parameters are arbitrary, we focus on jobs with uniform length. Our main result is a complete resolution of the deterministic complexity of this problem by showing that…
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## References

SHOWING 1-10 OF 43 REFERENCES
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM J. Comput.
• 2001
This work considers the following fundamental scheduling problem, and gives constant factor approximation algorithms for four variants of the problem, depending on the type of the machines and the weight of the jobs (identical vs. arbitrary).
Machine minimization for scheduling jobs with interval constraints
• Computer Science
45th Annual IEEE Symposium on Foundations of Computer Science
• 2004
Improved approximation factors for the number of machines needed to schedule all jobs in the continuous version of the problem are provided and the main result is an O(1)-approximation algorithm when the optimal number of Machines needed is bounded by a fixed constant.
Competitive Design and Analysis for Machine-Minimizing Job Scheduling Problem
ISAAC
• 2012
This work presents the first concrete result concerning online machine-minimizing job scheduling with arbitrary job arrival times and deadlines, and designs a 5.2-competitive online algorithm for this problem.
Improvements in throughout maximization for real-time scheduling
• Computer Science
STOC '00
• 2000
This work considers the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit, and provides algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al., while either having the same quality of approximation or improving it.
Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs
• Computer Science
STACS
• 2004
We study an online scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight. The goal is to maximize the weighted throughput, that
Resource Minimization Job Scheduling
APPROX-RANDOM
• 2009
This work builds on prior work to obtain a constant factor approximation algorithm for the resource-minimization job scheduling problem and shows an efficient algorithm for scheduling all jobs on O(({\rm \sc OPT})^2) machines has been shown.
Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help?
• Computer Science
Algorithmica
• 2003
A new algorithm MIXED-k with competitive ratio 1/(1 − (k/(k + 1)) k ) which approaches e/(e−1) ≈ 1.582 when k →∞ is given, thus answering an open problem raised by Chang and Yap, and showing that timesharing provably helps in giving better algorithms for this problem.
New hardness results for congestion minimization and machine scheduling
• Computer Science
STOC '04
• 2004
The hardness proof for congestion minimization holds even for the special case of the edge-disjoint paths problem, and the approximability of two natural NP-hard problems is studied.
Scheduling with Release Times and Deadlines on a Minimum Number of Machines