Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks
We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence g...
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| Vydáno v: | Advances in Operations Research Ročník 2011; číslo 2011; s. 201 - 220 |
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| Jazyk: | angličtina |
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Cairo, Egypt
Hindawi Limiteds
01.01.2011
Hindawi Puplishing Corporation Hindawi Publishing Corporation |
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| ISSN: | 1687-9147, 1687-9155 |
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| Abstract | We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter δ∈ℕ. We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time O(δ2)-approximation algorithm for the makespan minimization on processor networks with diameter δ.Erratum to “Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks”dx.doi.org/10.1155/2012/543215 |
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| AbstractList | We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth,with a fixed diameter δ ∈ . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time O δ2 -approximation algorithm for the makespan minimization on processor networks with diameter δ. We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter δ∈ℕ. We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time O(δ2)-approximation algorithm for the makespan minimization on processor networks with diameter δ. We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter δ∈ℕ. We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time O(δ2)-approximation algorithm for the makespan minimization on processor networks with diameter δ.Erratum to “Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks”dx.doi.org/10.1155/2012/543215 We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time -approximation algorithm for the makespan minimization on processor networks with diameter . |
| Author | Bouznif, M. Giroudeau, R. |
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| Cites_doi | 10.1016/S0167-5060(08)70356-X 10.1002/j.1538-7305.1966.tb01709.x 10.1016/j.tcs.2008.03.027 10.1145/321812.321815 10.1287/opre.45.1.145 10.1016/0166-218X(87)90042-4 10.1090/qam/102435 10.1007/s10288-010-0127-7 10.1137/0218016 |
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| Copyright | Copyright © 2011 M. Bouznif and R. Giroudeau. Attribution |
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| Editor | Liao, Ching-Jong |
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| References | (11) 2008; 401 (7) 1989; 18 (10) 1997; 45 (14) 1966; 45 (6) 1987; 18 LahlouC.Scheduling with unit processing and communication times on a ring network: approximation resultsProceedings of Europar1996New York, NY, USASpringer539542 ChrétienneP.PicouleauC.Scheduling Theory and Its Applications1995chapter 4Chichester, UKJohn Wiley & SonsScheduling with Communication Delays: A Survey BoudetV.CohenY.GiroudeauR.KonigJ. C.Complexity results for scheduling problem with non trivial topology of processors200606050LIRMMsubmitted to Rairo-RO (12) 1974; 21 MunierA.HanenC.An approximation algorithm for scheduling unitary tasks on m processors with communication delaysprivate communication, 1996 (13) 1958; 16 GareyM. R.JohnsonD. S.Computers and Intractability: A Guide to the Theory of 𝒩𝒫-Completeness1979San Francisco, Calif, USAW. H. Freemanx+338A Series of Books in the Mathematical Science519066 PicouleauC.UET-UCT schedules on arbitrary networks1994LITP, Blaise Pascal, Université Paris VI (3) 2011; 9 (1) 1979; 5 (13) 1997; 45 (1) 1958; 16 15 (5) 1979 (4) 1995 (8) 1966; 45 6 (7) 2011; 9 9 (11) 1996 (3) 1974; 21 10 |
| References_xml | – volume: 45 start-page: 145 issue: 1 year: 1997 end-page: 148 ident: 10 article-title: A heuristic for a scheduling problem with communication delays – reference: PicouleauC.UET-UCT schedules on arbitrary networks1994LITP, Blaise Pascal, Université Paris VI – reference: ChrétienneP.PicouleauC.Scheduling Theory and Its Applications1995chapter 4Chichester, UKJohn Wiley & SonsScheduling with Communication Delays: A Survey – volume: 18 start-page: 55 issue: 1 year: 1987 end-page: 71 ident: 6 article-title: UET scheduling with unit interprocessor communication delays – volume: 5 start-page: 287 year: 1979 end-page: 326 ident: 1 article-title: Optimization and approximation in deterministic sequencing and scheduling: a survey – volume: 9 start-page: 29 issue: 1 year: 2011 end-page: 48 ident: 3 article-title: Scheduling uet-tasks on a star network: complexity and approximation – volume: 45 start-page: 1563 year: 1966 end-page: 1581 ident: 14 article-title: Bounds for certain multiprocessing anomalies – reference: MunierA.HanenC.An approximation algorithm for scheduling unitary tasks on m processors with communication delaysprivate communication, 1996 – volume: 401 start-page: 107 issue: 1–3 year: 2008 end-page: 119 ident: 11 article-title: Complexity and approximation for precedence constrained scheduling problems with large communication delays – volume: 18 start-page: 244 issue: 2 year: 1989 end-page: 257 ident: 7 article-title: Scheduling precedence graphs in systems with interprocessor communication times – reference: BoudetV.CohenY.GiroudeauR.KonigJ. C.Complexity results for scheduling problem with non trivial topology of processors200606050LIRMMsubmitted to Rairo-RO – reference: GareyM. R.JohnsonD. S.Computers and Intractability: A Guide to the Theory of 𝒩𝒫-Completeness1979San Francisco, Calif, USAW. H. Freemanx+338A Series of Books in the Mathematical Science519066 – volume: 16 start-page: 87 year: 1958 end-page: 90 ident: 13 article-title: On a routing problem – reference: LahlouC.Scheduling with unit processing and communication times on a ring network: approximation resultsProceedings of Europar1996New York, NY, USASpringer539542 – volume: 21 start-page: 201 year: 1974 end-page: 206 ident: 12 article-title: The parallel evaluation of general arithmetic expressions – ident: 9 doi: 10.1016/S0167-5060(08)70356-X – year: 1995 ident: 4 – volume: 45 start-page: 1563 year: 1966 ident: 8 publication-title: Bell System Technical Journal doi: 10.1002/j.1538-7305.1966.tb01709.x – ident: 6 doi: 10.1016/j.tcs.2008.03.027 – year: 1979 ident: 5 – volume-title: Scheduling with unit processing and communication times on a ring network: approximation results year: 1996 ident: 11 – volume: 21 start-page: 201 year: 1974 ident: 3 publication-title: Journal of the Association for Computing Machinery doi: 10.1145/321812.321815 – volume: 45 start-page: 145 issue: 1 year: 1997 ident: 13 publication-title: Operations Research doi: 10.1287/opre.45.1.145 – ident: 15 doi: 10.1016/0166-218X(87)90042-4 – volume: 16 start-page: 87 year: 1958 ident: 1 publication-title: Quarterly of Applied Mathematics doi: 10.1090/qam/102435 – volume: 9 start-page: 29 issue: 1 year: 2011 ident: 7 publication-title: 4OR A Quarterly Journal of Operations Research doi: 10.1007/s10288-010-0127-7 – ident: 10 doi: 10.1137/0218016 |
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| Title | Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks |
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