• 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}
}
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… 
New Results on Online Resource Minimization
TLDR
This work provides the first constant-ratio competitive algorithm for the non-preemptive setting, which is of particular interest with regard to the known strong lower bound of n for the general problem, and gives an O(logn)-competitive algorithm forthe general preemptive problem, which improves upon a known O(log(pmax/pmin))-competitive algorithm.
An O(m^2 log m)-Competitive Algorithm for Online Machine Minimization
TLDR
This work considers the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates and designs a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.
The Power of Migration in Online Machine Minimization
TLDR
It is shown that in general no online algorithm can achieve a competitive ratio of f(m), for any function f, and a lower bound of Omega(log n) is derived.
Busy Time Scheduling on a Bounded Number of Machines (Extended Abstract)
TLDR
This paper develops the first correct constant factor online competitive algorithm for the case when g is unbounded, and gives a \(O(\log P)\) approximation for general g, where P is the ratio of maximum to minimum processing time.
Preemptive Online Machine Minimization
TLDR
This paper introduces two basic greedy algorithms, which do not do well on this problem, and analyzes two recent algorithms both proposed by Chen et al.
Online Scheduling of Time-Critical Tasks to Minimize the Number of Calibrations
Cost-Efficient Scheduling on Machines from the Cloud
TLDR
This work considers a scheduling problem where machines need to be rented from the cloud in order to process jobs and rents machines for machine-type dependent prices and for arbitrary durations.
Online machine minimization with lookahead
This paper studies the online machine minimization problem, where the jobs have real release times, uniform processing times and a common deadline. We investigate how the lookahead ability improves
An O(log m)-Competitive Algorithm for Online Machine Minimization
TLDR
This work considers the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates, and develops a feasible preemptive schedule for this problem.
...
...

References

SHOWING 1-10 OF 43 REFERENCES
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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?
TLDR
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
TLDR
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
TLDR
This paper shows that instances consisting of jobs with slack at most one can be solved efficiently in the SRDM problem and closes the resulting gap by showing that the problem already becomes NP-complete if slacks up to 2 are allowed.
Online vertex-weighted bipartite matching and single-bid budgeted allocations
TLDR
The main result is an optimal (1−1/e)-competitive randomized algorithm for general vertex weights that effectively solves the problem of online budgeted allocations in the case when an agent makes the same bid for any desired item, even if the bid is comparable to his budget.
...
...