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https://doi.org/10.4230/dagsem...
Article . 2010
License: CC BY
Data sources: Datacite
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Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold

Authors: Edmonds, Jeff;

Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold

Abstract

The goal is to prove a surprising lower bound for resource augmented nonclairvoyant algorithms for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time. Edmonds and Pruhs in SODA09 prove that for every $\e > 0$, there is an algorithm $\alg_{\e}$ that is $(1\!+\!\epsilon)$-speed $O({1 \over \e2})$-competitive. A problem, however, is that this algorithm $\alg_{\e}$ depends on $\e$. The goal is to prove that every fixed deterministic nonclairvoyant algorithm has a suboptimal speed threshold, namely for every (graceful) algorithm $\alg$, there is a threshold $1\!+\!\beta_{\alg}$ that is $\beta_{\alg} > 0$ away from being optimal such that the algorithm is $\Omega({1 \over \e \beta_{\alg}})$ competitive with speed $(1 \!+\! \beta_{\alg}) \!+\! \e$ and is $\omega(1)$ competitive with speed $1 \!+\! \beta_{\alg}$. I have worked very hard on it and have felt that I was close. The proof technique is to use Brouwer's fixed point theorem to break the cycle of needing to know which input will be given before one can know what the algorithm will do and needing to know what the algorithm will do before one can know which input to give. Every thing I have can be found at

Country
Germany
Subjects by Vocabulary

Dewey Decimal Classification: ddc:004

Keywords

Scheduling

3. Do not focus too little: Pi∈[nt] iρhi,ti ≥ (1 − β2 )nt (or βt d=ef 2[1 − n1t Pi∈[nt] iρhi,ti] ≤ β ). 1. Rx∈[0,1] fj(x)δx = Ri∈[0,j] jρhxj,ji h δji i = Ri∈[0,j] ρhxj,jiδi = 1. This uses constraint[2]. Increasing βj increase amount allocated to earlier jobs, which increases Loss. Oooooops. It decreases 1 − β2j .

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Funded by
NSERC
Project
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
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