Better permutations for the single-processor scheduling with time restrictions
In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer B ≥ 2 and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following B -constraint. For any real x , no unit time interval [ x , x + 1 ) is allowed to int...
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| Published in | Optimization letters Vol. 11; no. 4; pp. 715 - 724 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2017
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-016-1038-0 |
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| Abstract | In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer
B
≥
2
and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following
B
-constraint. For any real
x
, no unit time interval
[
x
,
x
+
1
)
is allowed to intersect more than
B
jobs. We show that there exists a permutation of the jobs which can be processed within a factor of
5
4
of the optimum (plus an additional small constant) when
B
≥
5
and this factor is best possible. When
B
=
3
,
4
, the corresponding factor equals
B
B
-
1
. Furthermore, we present an asymptotically optimal permutation for
B
=
2
. The results for
B
≥
4
improve the previous work on this problem. |
|---|---|
| AbstractList | In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer
B
≥
2
and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following
B
-constraint. For any real
x
, no unit time interval
[
x
,
x
+
1
)
is allowed to intersect more than
B
jobs. We show that there exists a permutation of the jobs which can be processed within a factor of
5
4
of the optimum (plus an additional small constant) when
B
≥
5
and this factor is best possible. When
B
=
3
,
4
, the corresponding factor equals
B
B
-
1
. Furthermore, we present an asymptotically optimal permutation for
B
=
2
. The results for
B
≥
4
improve the previous work on this problem. |
| Author | Chen, Guangting Ye, Feilang Chen, Yong Zhang, An |
| Author_xml | – sequence: 1 givenname: An surname: Zhang fullname: Zhang, An email: anzhang@hdu.edu.cn organization: Department of Mathematics, Hangzhou Dianzi University – sequence: 2 givenname: Feilang surname: Ye fullname: Ye, Feilang organization: Department of Mathematics, Hangzhou Dianzi University – sequence: 3 givenname: Yong surname: Chen fullname: Chen, Yong organization: Department of Mathematics, Hangzhou Dianzi University – sequence: 4 givenname: Guangting surname: Chen fullname: Chen, Guangting email: gtchen@hdu.edu.cn organization: Taizhou University |
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| Keywords | Single-processor scheduling Worst-case analysis Time restrictions |
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| References_xml | – volume: 17 start-page: 399 year: 2014 end-page: 403 ident: CR1 article-title: Single-processor scheduling with time restrictions publication-title: J. Sched. doi: 10.1007/s10951-013-0342-0 – volume: 230 start-page: 449 year: 2013 end-page: 463 ident: CR3 article-title: Parallel machine scheduling with additional resources: Notation, classification, models and solution methods publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2013.02.042 – ident: CR5 – volume: 8 start-page: 101 year: 2010 end-page: 104 ident: CR7 article-title: Operating room planning and scheduling solving a surgical case sequencing problem. 4OR-Q publication-title: J. Oper. Res. doi: 10.1007/s10288-009-0106-z – year: 2004 ident: CR2 publication-title: Handbook of scheduling – volume: 201 start-page: 921 year: 2010 end-page: 932 ident: CR8 article-title: Operating room planning and scheduling: a literature review publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2009.04.011 – volume: 31 start-page: 711 issue: 8 year: 1980 end-page: 723 ident: CR4 article-title: Two approaches to problems of resource allocation among project activities—a comparative study publication-title: J. Oper. Res. Soc. – volume: 5 start-page: 11 issue: 1 year: 1983 end-page: 24 ident: CR6 article-title: Scheduling subject to resource constraints: classification and complexity publication-title: Discret. Appl. Math. doi: 10.1016/0166-218X(83)90012-4 – volume: 38 start-page: 531 year: 2016 end-page: 540 ident: CR9 article-title: Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions publication-title: OR Spect. doi: 10.1007/s00291-016-0431-5 – ident: CR10 – volume: 201 start-page: 921 year: 2010 ident: 1038_CR8 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2009.04.011 – volume-title: Handbook of scheduling year: 2004 ident: 1038_CR2 doi: 10.1201/9780203489802 – volume: 230 start-page: 449 year: 2013 ident: 1038_CR3 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2013.02.042 – volume: 17 start-page: 399 year: 2014 ident: 1038_CR1 publication-title: J. Sched. doi: 10.1007/s10951-013-0342-0 – volume: 5 start-page: 11 issue: 1 year: 1983 ident: 1038_CR6 publication-title: Discret. Appl. Math. doi: 10.1016/0166-218X(83)90012-4 – volume: 31 start-page: 711 issue: 8 year: 1980 ident: 1038_CR4 publication-title: J. Oper. Res. Soc. – ident: 1038_CR5 – ident: 1038_CR10 doi: 10.1109/CoDIT.2014.6996900 – volume: 8 start-page: 101 year: 2010 ident: 1038_CR7 publication-title: J. Oper. Res. doi: 10.1007/s10288-009-0106-z – volume: 38 start-page: 531 year: 2016 ident: 1038_CR9 publication-title: OR Spect. doi: 10.1007/s00291-016-0431-5 |
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| Snippet | In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer
B
≥
2
and a set of jobs, we need to schedule the jobs... |
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| SubjectTerms | Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation |
| Title | Better permutations for the single-processor scheduling with time restrictions |
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