Complexity and approximation algorithms for two parallel dedicated machine scheduling with conflict constraints
We investigate two parallel dedicated machine scheduling with conflict constraints. The problem of minimizing the makespan has been shown to be NP-hard in the strong sense under the assumption that the processing sequence of jobs on one machine is given and fixed a priori. The problem without any fi...
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| Vydáno v: | Theoretical computer science Ročník 941; s. 167 - 179 |
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Elsevier B.V
04.01.2023
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | We investigate two parallel dedicated machine scheduling with conflict constraints. The problem of minimizing the makespan has been shown to be NP-hard in the strong sense under the assumption that the processing sequence of jobs on one machine is given and fixed a priori. The problem without any fixed sequence was previously recognized as weakly NP-hard. In this paper, we first present a 95-approximation algorithm for the problem with a fixed sequence. Then we show that the tight approximation ratios of the algorithm are 74 and 53 for two subproblems which remain strongly NP-hard. We also send an improved algorithm with approximation ratio 3−2≈1.586 for one subproblem. Finally, we prove that the problem without any fixed sequence is actually strongly NP-hard, and design a 53-approximation algorithm.
•Consider the problem of scheduling with conflict constraints on two parallel dedicated machines.•Present a 95-approximation algorithm for the strongly NP-hard case where jobs on one machine have a fixed processing sequence, and give improvements to its hard subproblems.•Prove that the problem without any fixed sequence is strongly NP-hard too and propose a 53-approximation algorithm. |
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| AbstractList | We investigate two parallel dedicated machine scheduling with conflict constraints. The problem of minimizing the makespan has been shown to be NP-hard in the strong sense under the assumption that the processing sequence of jobs on one machine is given and fixed a priori. The problem without any fixed sequence was previously recognized as weakly NP-hard. In this paper, we first present a 95-approximation algorithm for the problem with a fixed sequence. Then we show that the tight approximation ratios of the algorithm are 74 and 53 for two subproblems which remain strongly NP-hard. We also send an improved algorithm with approximation ratio 3−2≈1.586 for one subproblem. Finally, we prove that the problem without any fixed sequence is actually strongly NP-hard, and design a 53-approximation algorithm.
•Consider the problem of scheduling with conflict constraints on two parallel dedicated machines.•Present a 95-approximation algorithm for the strongly NP-hard case where jobs on one machine have a fixed processing sequence, and give improvements to its hard subproblems.•Prove that the problem without any fixed sequence is strongly NP-hard too and propose a 53-approximation algorithm. |
| Author | Chen, Guangting Wang, Xing Zhang, Liang Chen, Yong Zhang, An |
| Author_xml | – sequence: 1 givenname: An orcidid: 0000-0002-2622-5158 surname: Zhang fullname: Zhang, An email: anzhang@hdu.edu.cn organization: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China – sequence: 2 givenname: Liang surname: Zhang fullname: Zhang, Liang organization: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China – sequence: 3 givenname: Yong surname: Chen fullname: Chen, Yong organization: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China – sequence: 4 givenname: Guangting surname: Chen fullname: Chen, Guangting email: gtchen@hdu.edu.cn organization: Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China – sequence: 5 givenname: Xing surname: Wang fullname: Wang, Xing organization: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China |
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| Cites_doi | 10.1016/j.tcs.2019.01.038 10.1016/0304-3975(96)00031-X 10.1016/0166-218X(85)90027-7 10.1007/s10951-008-0089-1 10.1016/0885-064X(91)90006-J 10.1016/j.cor.2011.04.014 10.1016/S0377-2217(02)00246-1 10.1016/j.cie.2018.07.035 10.1016/S0890-5401(02)00032-9 10.1016/S0890-5401(02)00028-7 10.1007/BF01202286 10.1016/j.ejor.2014.07.003 10.1137/0204015 10.1016/0304-3975(95)00057-4 |
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| Keywords | Conflict graph NP-hard Parallel dedicated machines Approximation algorithm |
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| SubjectTerms | Approximation algorithm Conflict graph NP-hard Parallel dedicated machines |
| Title | Complexity and approximation algorithms for two parallel dedicated machine scheduling with conflict constraints |
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