Optimality of HLF for scheduling divide-and-conquer UET task graphs on identical parallel processors
The problem of scheduling a set of n unit execution time (UET) tasks subject to precedence constraints on m identical parallel processors is known to be N P -hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class...
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| Vydané v: | Discrete optimization Ročník 6; číslo 1; s. 79 - 91 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.02.2009
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| ISSN: | 1572-5286, 1873-636X |
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| Abstract | The problem of scheduling a set of
n
unit execution time (UET) tasks subject to precedence constraints on
m
identical parallel processors is known to be
N
P
-hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class of divide-and-conquer graphs that naturally models the execution of the recursive control abstraction of divide-and-conquer algorithms. We prove that the Highest Level First (HLF) strategy minimizes the schedule length for this class, thus settling a conjecture of Rayward-Smith and Clark. |
|---|---|
| AbstractList | The problem of scheduling a set of
n
unit execution time (UET) tasks subject to precedence constraints on
m
identical parallel processors is known to be
N
P
-hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class of divide-and-conquer graphs that naturally models the execution of the recursive control abstraction of divide-and-conquer algorithms. We prove that the Highest Level First (HLF) strategy minimizes the schedule length for this class, thus settling a conjecture of Rayward-Smith and Clark. |
| Author | Kubiak, Wieslaw Potts, Chris Rebaine, Djamal |
| Author_xml | – sequence: 1 givenname: Wieslaw surname: Kubiak fullname: Kubiak, Wieslaw email: wkubiak@mun.ca organization: Faculty of Business Administration, Memorial University, St. John’s, Canada – sequence: 2 givenname: Djamal surname: Rebaine fullname: Rebaine, Djamal organization: Département d’Informatique et de Mathématique, Université du Québec à Chicoutimi, Québec, Canada – sequence: 3 givenname: Chris surname: Potts fullname: Potts, Chris organization: School of Mathematics, University of Southampton, Southampton, UK |
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| Cites_doi | 10.1287/opre.9.6.841 10.1137/0604011 10.1016/S0167-6377(99)00003-6 10.1137/S0895480101394999 10.1007/978-94-009-7801-0_22 10.1137/0606066 10.1007/BF00288685 10.1137/0211023 10.1137/0214047 10.1016/0196-6774(84)90039-7 |
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| Keywords | Divide-and-conquer graph Makespan HLF Complexity Identical parallel processors |
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| References | Dolev, Warmuth (b6) 1985; 14 Hu (b10) 1961; 9 Garey, Johnson, Tarjan, Yannakakis (b8) 1983; 4 Dolev, Warmuth (b7) 1982; 5 Horowitz, Sahni (b9) 1978 Moukrim (b11) 1999; 24 V.J. Rayward-Smith, A.J. Clark, Scheduling Theory Applied to Divide-and-Conquer Task Systems on Identical Parallel Machines, in: C.R. Jessehope, K.D. Reinartz (Eds.), in: Conpar’88, BCS Workshop Series, Cambridge University Press, Cambridge, 1989 Coffman, Graham (b3) 1972; 1 Dasgupta, Papadimitriou, Vazirani (b4) 2006 Dolev, Warmuth (b5) 1985; 6 J. Bruno, Deterministic and stochastic scheduling problems with treelike precedence constraints, in: NATO conference, Durham, England, 1981 Valdes, Tarjan, Lawler (b13) 1982; 11 Chardon, Moukrim (b2) 2005; 19 Coffman (10.1016/j.disopt.2008.09.001_b3) 1972; 1 10.1016/j.disopt.2008.09.001_b1 Hu (10.1016/j.disopt.2008.09.001_b10) 1961; 9 Dolev (10.1016/j.disopt.2008.09.001_b5) 1985; 6 Moukrim (10.1016/j.disopt.2008.09.001_b11) 1999; 24 Chardon (10.1016/j.disopt.2008.09.001_b2) 2005; 19 Valdes (10.1016/j.disopt.2008.09.001_b13) 1982; 11 Dasgupta (10.1016/j.disopt.2008.09.001_b4) 2006 Dolev (10.1016/j.disopt.2008.09.001_b6) 1985; 14 10.1016/j.disopt.2008.09.001_b12 Garey (10.1016/j.disopt.2008.09.001_b8) 1983; 4 Horowitz (10.1016/j.disopt.2008.09.001_b9) 1978 Dolev (10.1016/j.disopt.2008.09.001_b7) 1982; 5 |
| References_xml | – volume: 6 start-page: 665 year: 1985 end-page: 687 ident: b5 article-title: Profile scheduling of opposing forest and level orders publication-title: SIAM J. Algebr. Discrete Methods – volume: 5 start-page: 48 year: 1982 end-page: 59 ident: b7 article-title: Scheduling precedence graphs with bounded height publication-title: J. Algorithms – volume: 11 start-page: 298 year: 1982 end-page: 317 ident: b13 article-title: The recognition of series parallel digraphs publication-title: SIAM J. Comput. – volume: 1 start-page: 200 year: 1972 end-page: 213 ident: b3 article-title: Optimal scheduling for two-processor systems publication-title: Acta Inform. – volume: 9 start-page: 841 year: 1961 end-page: 848 ident: b10 article-title: Parallel sequencing and assembly line problems publication-title: Oper. Res. – volume: 19 start-page: 109 year: 2005 end-page: 121 ident: b2 article-title: The Coffman–Graham algorithm optimally solves UET task systems with over-interval orders publication-title: SIAM J. Discrete Math. – volume: 24 start-page: 91 year: 1999 end-page: 95 ident: b11 article-title: Optimal scheduling on parallel machines for a new order class publication-title: Oper. Res. Lett. – year: 1978 ident: b9 article-title: Fundamentals of Computer Algorithms – reference: V.J. Rayward-Smith, A.J. Clark, Scheduling Theory Applied to Divide-and-Conquer Task Systems on Identical Parallel Machines, in: C.R. Jessehope, K.D. Reinartz (Eds.), in: Conpar’88, BCS Workshop Series, Cambridge University Press, Cambridge, 1989 – reference: J. Bruno, Deterministic and stochastic scheduling problems with treelike precedence constraints, in: NATO conference, Durham, England, 1981 – year: 2006 ident: b4 article-title: Algorithms – volume: 14 start-page: 638 year: 1985 end-page: 657 ident: b6 article-title: Scheduling flat graphs publication-title: SIAM J. Comput. – volume: 4 start-page: 72 year: 1983 end-page: 93 ident: b8 article-title: Scheduling opposing forests publication-title: SIAM J. Algebr. Discrete Methods – volume: 9 start-page: 841 year: 1961 ident: 10.1016/j.disopt.2008.09.001_b10 article-title: Parallel sequencing and assembly line problems publication-title: Oper. Res. doi: 10.1287/opre.9.6.841 – volume: 4 start-page: 72 year: 1983 ident: 10.1016/j.disopt.2008.09.001_b8 article-title: Scheduling opposing forests publication-title: SIAM J. Algebr. Discrete Methods doi: 10.1137/0604011 – ident: 10.1016/j.disopt.2008.09.001_b12 – year: 2006 ident: 10.1016/j.disopt.2008.09.001_b4 – year: 1978 ident: 10.1016/j.disopt.2008.09.001_b9 – volume: 24 start-page: 91 year: 1999 ident: 10.1016/j.disopt.2008.09.001_b11 article-title: Optimal scheduling on parallel machines for a new order class publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(99)00003-6 – volume: 19 start-page: 109 issue: 1 year: 2005 ident: 10.1016/j.disopt.2008.09.001_b2 article-title: The Coffman–Graham algorithm optimally solves UET task systems with over-interval orders publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480101394999 – ident: 10.1016/j.disopt.2008.09.001_b1 doi: 10.1007/978-94-009-7801-0_22 – volume: 6 start-page: 665 year: 1985 ident: 10.1016/j.disopt.2008.09.001_b5 article-title: Profile scheduling of opposing forest and level orders publication-title: SIAM J. Algebr. Discrete Methods doi: 10.1137/0606066 – volume: 1 start-page: 200 year: 1972 ident: 10.1016/j.disopt.2008.09.001_b3 article-title: Optimal scheduling for two-processor systems publication-title: Acta Inform. doi: 10.1007/BF00288685 – volume: 11 start-page: 298 year: 1982 ident: 10.1016/j.disopt.2008.09.001_b13 article-title: The recognition of series parallel digraphs publication-title: SIAM J. Comput. doi: 10.1137/0211023 – volume: 14 start-page: 638 issue: 3 year: 1985 ident: 10.1016/j.disopt.2008.09.001_b6 article-title: Scheduling flat graphs publication-title: SIAM J. Comput. doi: 10.1137/0214047 – volume: 5 start-page: 48 year: 1982 ident: 10.1016/j.disopt.2008.09.001_b7 article-title: Scheduling precedence graphs with bounded height publication-title: J. Algorithms doi: 10.1016/0196-6774(84)90039-7 |
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unit execution time (UET) tasks subject to precedence constraints on
m
identical parallel processors is known to be
N
P... |
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| SubjectTerms | Complexity Divide-and-conquer graph HLF Identical parallel processors Makespan |
| Title | Optimality of HLF for scheduling divide-and-conquer UET task graphs on identical parallel processors |
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