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Dedicated Scheduling of Biprocessor Tasks to Minimize Mean Flow Time

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Parallel Processing and Applied Mathematics (PPAM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2328))

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Abstract

This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to minimize mean flow time. Since the general problem is strongly NP-hard, we assume some restrictions on task lengths and the structure of associated scheduling graphs. Of particular interest are acyclic graphs. In this way we identify a borderline between NP-hard and polynomially solvable special cases.

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References

  1. Coffman, Jr., E.G., Garey, M.R., Johnson, D.S., LaPaugh, A.S.: Scheduling file transfers. SIAM J. Comput. 14 (1985) 744–780

    Article  MathSciNet  MATH  Google Scholar 

  2. Cole, R., Ost, K., Schirra, S., Edge-coloring bipartite graphs in O(E logD) time. Combinatorica 21 (2001) 5–12

    Article  MathSciNet  MATH  Google Scholar 

  3. Dobson, G., Karmarkar, U.S.: Simultaneous resourse scheduling to minimize weighted flow times. Oper. Res. 37 (1989) 592–600

    Article  MathSciNet  MATH  Google Scholar 

  4. Drozdowski, M.: Scheduling multiprocessor tasks-An overview. Euro. J. Oper. Res. 94 (1996) 215–230

    Article  MATH  Google Scholar 

  5. Drozdowski, M., Dell’Olmo, P.: Scheduling multiprocessor tasks for mean flow time criterion. Comp. Oper. Res. 27 (2000) 571–585

    Article  MathSciNet  MATH  Google Scholar 

  6. Gehringer, E.F., Siewiorek, D.P., Segall, Z.: Parallel Processing: The Cm* Experience. Digital Press, Bedford (1987)

    Google Scholar 

  7. Giaro, K., Kubale, M., MaFlafiejski, M., Piwakowski, K.: Chromatic scheduling of dedicated 2-processor UET tasks to minimize mean flow time. Proc. ETFA’99, Barcelona (1999) 343–347

    Google Scholar 

  8. Giaro, K., Kubale, M.: Edge-chromatic sum of trees and bounded cyclicity graphs. Inf. Process. Lett. 75 (2000) 65–69

    Article  MathSciNet  Google Scholar 

  9. Giaro, K., Kubale, M., Piwakowski, K.: Complexity results on open shop scheduling to minimize weighted mean flow time of operations. (in preparation)

    Google Scholar 

  10. Halldórsson, M.M., Kortsarz, G., Proskurowski, A., Salman, R., Shachnai, H., Telle, J.A., Multicoloring trees. Computing and Combinatorics Conference, Tokyo (1999), Lecture Notes in Computer Science 1627 (1999) 271–280

    Chapter  Google Scholar 

  11. Hoogeveen, J.A., van de Velde, S.L., Veltman, B.: Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Disc. Appl. Math. 55 (1994) 259–272

    Article  MATH  Google Scholar 

  12. Krawczyk, H., Kubale, M.: An approximation algorithm for diagnostic test scheduling in multicomputer systems. IEEE Trans. Comput. 34 (1985) 869–872

    Article  Google Scholar 

  13. Kubale, M.: The complexity of scheduling independent two-processor tasks on dedicated processors. Inf. Process. Lett. 24 (1987) 141–147

    Article  MathSciNet  MATH  Google Scholar 

  14. Kubale, M.: Preemptive versus nonpreemptive scheduling of biprocessor tasks on dedicated processors. Euro. J. Oper. Res. 94 (1996) 242–251

    Article  MATH  Google Scholar 

  15. Kubale, M., Piwakowski, K.: A linear algorithm for edge coloring of binomial trees. Disc. Math. 150 (1996) 247–256

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, X., Nishizeki, T.: Algorithms for the cost edge-coloring of tress. Lecture Notes in Computer Science 2108 (2001) 288–297

    Google Scholar 

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Author information

Authors and Affiliations

  1. Foundations of Informatics Dept., Technical University of Gdańsk, Narutowicza 11/12, 80-952, Gdańsk, Poland

    Krzysztof Giaro, Marek Kubale, Michał Małafiejski & Konrad Piwakowski

Authors
  1. Krzysztof Giaro
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  2. Marek Kubale
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  3. Michał Małafiejski
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  4. Konrad Piwakowski
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, 122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

  3. Computer Science Department, Oklahoma State University, 700 N. Greenwood Ave., Tulsa, OK, 74106, USA

    Marcin Paprzycki

  4. DTU, UNI-C, Danish Computing Centre for Research and Education, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2002 Springer-Verlag Berlin Heidelberg

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Giaro, K., Kubale, M., Małafiejski, M., Piwakowski, K. (2002). Dedicated Scheduling of Biprocessor Tasks to Minimize Mean Flow Time. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_10

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  • DOI: https://doi.org/10.1007/3-540-48086-2_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43792-5

  • Online ISBN: 978-3-540-48086-0

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