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Scheduling for Parallel Processing

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Abstract

In this chapter, we study the scheduling model of parallel tasks. It is assumed that a parallel task may use more than one processor at the same time. This relaxation departs from one of the classic scheduling assumptions (Sect. 4.1). Before proceeding with the further presentation let us comment on the naming conventions. Different names have been used for the parallel tasks and their special cases. These were concurrent, multiprocessor, multiversion, malleable, moldable, rigid, and parallel tasks [29, 86, 100, 175]. One name often denotes different things. We adopt, and slightly extend, the naming convention of [100]. Reviews of parallel task scheduling can be found, e.g., in [32, 39, 81, 82, 100, 227]. Some results on the complexity of parallel task scheduling problems are collected in [42]. Proceedings of JSSPP workshop [92] are a rich source of knowledge on parallel task scheduling.

This chapter is organized as follows. In the next section, we present practical reasons for introducing parallel task model. In Sect. 5.2 we formally define variants of the model, which are studied in the following sections. In the last section, we discuss odds against, and in favor of the parallel task model.

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References

  1. F. Afrati, E. Bampis, A. Fishkin, K. Jansen, and C. Kenyon. Scheduling to minimize the average completion time of dedicated tasks. In S. Kapoor and S. Prasad, editors, Proceedings of 20th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’00). LNCS, volume 1974, pages 454–464, 2000.

    Google Scholar 

  2. M. Ahuja and Y. Zhu. An O(nlogn) feasibility algorithm for preemptive scheduling of n independent jobs on a hypercube. Information Processing Letters, 35(1):7–11, 1990.

    MATH  MathSciNet  Google Scholar 

  3. A. Al-Dhelaan and B. Bose. A new strategy for processors allocation in an n-cube multiprocessor. In Proceedings of 8th Annual International Phoenix Conference on Computers and Communications, pages 114–118, 1989.

    Google Scholar 

  4. A.K. Amoura, E. Bampis, C. Kenyon, and Y. Manoussakis. Scheduling independent multiprocessor tasks. Algorithmica, 32(2):247–261, 2002.

    MATH  MathSciNet  Google Scholar 

  5. A.K. Amoura. A note on scheduling multiprocessor tasks with precedence constraints on parallel processors. Information Processing Letters, 63(3):119–122, 1997.

    MathSciNet  Google Scholar 

  6. A.K. Amoura, E. Bampis, Y. Manoussakis, and Zs. Tuza. A comparison of heuristics for scheduling multiprocessor tasks on three dedicated processors. Parallel Computing, 25(1):49–61, 1999.

    Google Scholar 

  7. S.V. Anastasiadis and K.C. Sevcik. Parallel application scheduling on networks of workstations. Journal of Parallel and Distributed Computing, 43(2):109–124, 1997.

    Google Scholar 

  8. M.J. Atallah, C.L. Black, D.C. Marinescu, H.J. Siegel, and T.L. Casavant. Models and algorithms for coscheduling compute-intensive tasks on a network of workstations. Journal of Parallel and Distributed Computing, 16(4):319–327, 1992.

    MATH  Google Scholar 

  9. D. Babbar and P. Krueger. On-line hard real-time scheduling of parallel tasks on partitionable multiprocessors. In Proceedings of International Conference on Parallel Processing (ICPP’94), pages II–29–II–38. IEEE Computer Society, Los Alamitos, CA, USA, 1994.

    Google Scholar 

  10. D. Babbar and P. Krueger. A performance comparison of processor allocation and job scheduling algorithms for mesh-connected multiprocessors. In Proceedings of 6th IEEE Symposium on Parallel and Distributed Processing (SPDP’94), pages 46–53, 1994.

    Google Scholar 

  11. E. Bampis and A. Kononov. On the approximability of scheduling multiprocessor tasks with time-dependent processor and time requirements. In Proceedings of 15th International Parallel and Distributed Processing Symposium (IPDPS’01), pages 2144–2151, 2001.

    Google Scholar 

  12. S. Bani-Mohammad, M. Ould-Khaoua, I. Ababneh, and L.M. Mackenzie. Non-contiguous processor allocation strategy for 2D mesh connected multicomputers based on sub-meshes available for allocation. In Proceedings of 12th International Conference on Parallel and Distributed Systems (ICPADS’06), pages 41–48, 2006.

    Google Scholar 

  13. P. Baptiste. A note on scheduling multiprocessor tasks with identical processing times. Computers and Operations Research, 30(13):2071–2078, 2003.

    MATH  MathSciNet  Google Scholar 

  14. P. Baptiste and B. Schieber. A note on scheduling tall/small multiprocessor tasks with unit processing time to minimize maximum tardiness. Journal of Scheduling, 6(4):395–404, 2003.

    MATH  MathSciNet  Google Scholar 

  15. A. Bar-Noy, R. Canetti, S. Kutten, Y. Mansour, and B. Schieber. Bandwidth allocation with preemption. SIAM Journal on Computing, 28(5):1806–1828, 1999.

    MATH  MathSciNet  Google Scholar 

  16. K. Belkhale and P. Banerjee. An approximate algorithm for the partitionable independent task scheduling problem. In Proceedings of International Conference on Parallel Processing (ICPP’90), volume 1, pages 72–75, 1990.

    Google Scholar 

  17. M.A. Bender, D.P. Bunde, E.D. Demaine, S.P. Fekete, V.J. Leung, H. Meijer, and C.A. Phillips. Communication-aware processor allocation for supercomputers. http://arxiv.org/PS_cache/cs/pdf/0407/0407058v2.pdf, 2005 [online accessed 21 October 2007].

  18. S. Bhattacharya and W.-T. Tsai. Lookahead processor allocation in mesh-connected massively parallel multicomputer. In Proceedings of 8th International Parallel Processing Symposium (IPPS’94), pages 868–875, 1994.

    Google Scholar 

  19. L. Bianco, J. Błażewicz, P. Dell’Olmo, and M. Drozdowski. Scheduling preemptive multiprocessor tasks on dedicated processors. Performance Evaluation, 20(4):361–371, 1994.

    MATH  MathSciNet  Google Scholar 

  20. L. Bianco, J. Błażewicz, P. Dell’Olmo, and M. Drozdowski. Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors. Annals of Operations Research, 58(7):493–517, 1995.

    MATH  MathSciNet  Google Scholar 

  21. L. Bianco, J. Błażewicz, P. Dell’Olmo, and M. Drozdowski. Preemptive multiprocessor task scheduling with release times and time windows. Annals of Operations Research, 70:43–55, 1997.

    MATH  MathSciNet  Google Scholar 

  22. L. Bianco, P. Dell’Olmo, S. Giordani, and M. G. Speranza. Minimizing makespan in a multimode multiprocessor shop scheduling problem. Naval Research Logistics, 46(8):893–911, 1999.

    MATH  MathSciNet  Google Scholar 

  23. L. Bianco, P. Dell’Olmo, and M.G. Speranza. Nonpreemptive scheduling of independent tasks with prespecified processor allocations. Naval Research Logistics, 41(7):959–971, 1994.

    MATH  Google Scholar 

  24. L. Bianco, P. Dell’Olmo, and M.G. Speranza. Scheduling independent tasks with multiple modes. Discrete Applied Mathematics, 62(1–3):35–50, 1995.

    MATH  MathSciNet  Google Scholar 

  25. S. Bischof. Efficient Algorithms for On-Line Scheduling and Load Distribution in Parallel Systems. Ph.D. thesis, Lehrstuhl für Effiziente Algorithmen der Technischen Universität München, 1999. http://tumb1.biblio.tu-muenchen.de/publ/diss/in/1999/bischof.pdf [online accessed 03 October 2007].

  26. S. Bischof and E.W. Mayr. On-line scheduling of parallel jobs with runtime restrictions. Theoretical Computer Science, 268(1):67–90, 2001.

    MATH  MathSciNet  Google Scholar 

  27. J. Błażewicz, P. Dell’Olmo, M. Drozdowski, and P. Mączka. Scheduling multiprocessor tasks on parallel processors with limited availability. European Journal of Operational Research, 149(2):377–389, 2003.

    MATH  MathSciNet  Google Scholar 

  28. J. Błażewicz, P. Dell’Olmo, M. Drozdowski, and M.G. Speranza. Scheduling multiprocessor tasks on three dedicated processors. Information Processing Letters, 41:275–280, 1992. Corrigendum: IPL 49, 1994, 269-270.

    Google Scholar 

  29. J. Błażewicz, M. Drabowski, and J. Wêglarz. Scheduling multiprocessor tasks to minimize schedule length. IEEE Transactions on Computers, 35(5):389–393, 1986.

    MATH  Google Scholar 

  30. J. Błażewicz, M. Drozdowski, G. Schmidt, and D. de Werra. Scheduling independent multiprocessor tasks on a uniform k-processor system. Parallel Computing, 20(1):15–28, 1994.

    MATH  MathSciNet  Google Scholar 

  31. J. Błażewicz, M. Drozdowski, D. de Werra, and J. Wêglarz. Scheduling independent multiprocessor tasks before deadlines. Discrete Applied Mathematics, 65(1–3):81–96, 1996.

    MATH  MathSciNet  Google Scholar 

  32. J. Błażewicz, K. Ecker, E.Pesch, G. Schmidt, and J. Węglarz. Scheduling Computer and Manufacturing Processes. Springer, Heidelberg, New York, 1996.

    Google Scholar 

  33. J. Błażewicz, M. Kovalyov, M. Machowiak, D. Trystram, and J. Węglarz. Preemptable malleable task scheduling problem. IEEE Transactions on Computers, 55(4):486–490, 2006.

    Google Scholar 

  34. J. Błażewicz, J.K. Lenstra, and A.H.G. Rinnoy Kan. Scheduling subject to resource constraints: Classification and complexity. Discrete Applied Mathematics, 5:11–24, 1983.

    MATH  MathSciNet  Google Scholar 

  35. J. Błażewicz and Z. Liu. Scheduling multiprocessor tasks with chain constraints. European Journal of Operational Research, 94:231–241, 1996.

    MATH  Google Scholar 

  36. J. Błażewicz and Z. Liu. Linear and quadratic algorithms for scheduling chains and opposite chains. European Journal of Operational Research, 137(2):248–264, 2002.

    MATH  MathSciNet  Google Scholar 

  37. J. Błażewicz, M. Machowiak, J. Węglarz, M. Kovalyov, and D. Trystram. Scheduling malleable tasks on parallel processors to minimize the makespan. Annals of Operations Research, 129:65–80, 2004.

    MATH  MathSciNet  Google Scholar 

  38. G. Bozoki and J.-P. Richard. A branch-and-bound algorithm for the continuous-process job-shop scheduling problem. AIIE Transactions, 2(3):246–252, 1970.

    Google Scholar 

  39. P. Brucker. Scheduling Algorithms. Springer, Berlin, 1995.

    MATH  Google Scholar 

  40. P. Brucker and A. Krämer. Shop scheduling problems with multiprocessor tasks and dedicated processors. Annals of Operations Research: Mathematics of Industrial Systems I, 57:13–27, 1995.

    MATH  Google Scholar 

  41. P. Brucker and A. Krämer. Polynomial algorithms for resource constrained and multiprocessor task scheduling problems. European Journal of Operational Research, 90(2):214–226, 1996.

    MATH  Google Scholar 

  42. P. Brucker and S. Knust. Complexity results for scheduling problems. http://www.mathematik.uni-osnabrueck.de/research/OR/class/, 2006 [online accessed 9 November 2006].

  43. P. Brucker, S. Knust, D. Roper, and Y. Zinder. Scheduling UET task systems with concurrency on two parallel identical processors. Mathematical Methods of Operations Research, 52(3):369–387, 2000.

    MATH  MathSciNet  Google Scholar 

  44. X. Cai, C.-Y. Lee, and C.-L. Li. Minimizing total completion time in two-processor task systems with prespecified processor allocations. Naval Research Logistics, 45(2):231–242, 1998.

    MATH  MathSciNet  Google Scholar 

  45. X. Cai, C.-Y. Lee, and T.-L. Wong. Multiprocessor task scheduling to minimize the maximum tardiness and the total completion time. IEEE Transactions on Robotics and Automation, 16(6):824–830, 2000.

    Google Scholar 

  46. M. Caramia, P. Dell’Olmo, and A. Iovanella. On-line algorithms for multiprocessor task scheduling with ready times. Foundations of Computing and Decision Sciences, 26(3):197–214, 2001.

    MATH  MathSciNet  Google Scholar 

  47. C.-Y. Chang and P. Mohapatra. An adaptive job allocation method for multicomputer systems. In Proceedings of 16th International Conference on Distributed Computing Systems (ICDCS’96), pages 224–231, 1996.

    Google Scholar 

  48. C.-Y. Chang and P. Mohapatra. Performance improvement of allocation schemes for mesh-connected computers. Journal of Parallel and Distributed Computing, 52(1):40–68, 1998.

    MATH  Google Scholar 

  49. C.-Y. Chang and P. Mohapatra. Processor allocation using user directives in mesh-connected multicomputer systems. In Proceedings of 5th International Conference on High Performance Computing (HIPC’98), pages 302–309, 1998.

    Google Scholar 

  50. G.-I. Chen and T.-H. Lai. Preemptive scheduling of independent jobs on a hypercube. Information Processing Letters, 28(4):201–206, 1988.

    MATH  MathSciNet  Google Scholar 

  51. G.-I. Chen and T.-H. Lai. Scheduling independent jobs on partitionable hypercubes. Journal of Parallel and Distributed Computing, 12(1):74–78, 1991.

    MATH  MathSciNet  Google Scholar 

  52. J. Chen and C.-Y. Lee. General multiprocessor task scheduling. Naval Research Logistics, 46(1):57–74, 1999.

    MATH  MathSciNet  Google Scholar 

  53. J. Chen and A. Miranda. A polynomial time approximation scheme for general multiprocessor job scheduling. SIAM Journal on Computing, 31(1):1–17, 2001.

    MATH  MathSciNet  Google Scholar 

  54. M.-S. Chen and K.G. Shin. Processor allocation in an n-cube multiprocessor using gray codes. IEEE Transactions on Computers, 36(12):1396–1407, 1987.

    MathSciNet  Google Scholar 

  55. M.-S. Chen and K.G. Shin. Subcube allocation and task migration in hypercube multiprocessors. IEEE Transactions on Computers, 39(9):1146–1155, 1990.

    MathSciNet  Google Scholar 

  56. S.H. Chiang, R.K. Mansharamani, and M.K. Vernon. Use of application characteristics and limited preemption for run-to-completion parallel processor scheduling policies. In ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, pages 33–44, 1994.

    Google Scholar 

  57. G.-M. Chiu and S.-K. Chen. An efficient submesh allocation scheme for two-dimensional meshes with little overhead. IEEE Transactions on Parallel and Distributed Systems, 10(5):471–486, 1999.

    Google Scholar 

  58. H. Choo, S.-M. Yoo, and H. Y. Youn. Processor scheduling and allocation for 3D torus multicomputer systems. IEEE Transactions on Parallel and Distributed Systems, 11(5):475–484, 2000.

    Google Scholar 

  59. A.N. Choudhary, B. Narahari, D.M. Nicol, and R. Simha. Optimal processor assignment for a class of pipelined computations. IEEE Transactions on Parallel and Distributed Systems, 5(4):439–445, 1994.

    Google Scholar 

  60. Ch.Rapine, I. Scherson, and D. Trystram. On-line scheduling of parallelizable jobs. In D. Pritchard and J. Reeve, editors, Proceedings of Euro-Par 1998. LNCS, volume 1470, pages 322–327. Springer, Berlin, 1998.

    Google Scholar 

  61. P.-J. Chuang and N.-F. Tzeng. An efficient submesh allocation strategy for mesh computer systems. In Proceedings of 11th International Conference on Distributed Computing Systems, pages 256–263. IEEE, Computer Society, Los Alamitos, CA, USA, 1991.

    Google Scholar 

  62. P.-J. Chuang and N.-F. Tzeng. A fast recognition-complete processor allocation strategy for hypercube computers. IEEE Transactions on Computers, 41(4):467–479, 1992.

    Google Scholar 

  63. W. Cirne and F. Berman. A model for moldable supercomputer jobs. In Proceedings of 15th International Parallel and Distributed Processing Symposium (IPDPS’01), page 10059b. IEEE, Computer Society, Los Alamitos, CA, USA, 2001.

    Google Scholar 

  64. J. A. Cobb, M. G. Gouda, and A. El Nahas. Time-shift scheduling: Fair scheduling of flows in high speed networks. In Proceedings of 1996 International Conference on Network Protocols (ICNP ’96), pages 6–13, 1996.

    Google Scholar 

  65. E.G. Coffman Jr., M.R. Garey, and D.S. Johnson. Bin packing with divisible item sizes. Journal of Complexity, 14(3):406–428, 1987.

    MathSciNet  Google Scholar 

  66. E.G. Coffman Jr., M.R. Garey, D.S. Johnson, and A.S. LaPaugh. Scheduling file transfers. SIAM Journal on Computing, 14(3):744–780, 1985.

    MATH  MathSciNet  Google Scholar 

  67. G. Confessore, P. Dell’Olmo, and S. Giordani. Complexity and approximation results for scheduling multiprocessor tasks on a ring. Discrete Applied Mathematics, 133(1–3):29–44, 2004.

    MathSciNet  Google Scholar 

  68. G.L. Craig, C.R. Kime, and K.K. Saluja. Test scheduling and control for VLSI built-in self-test. IEEE Transactions on Computers, 37(9):1099–1109, 1988.

    Google Scholar 

  69. F.A. Barbosa da Silva and I.D. Scherson. Improving throughput and utilization in parallel machines through concurrent gang. In Proceedings of 14th International Parallel and Distributed Processing Symposium (IPDPS’00), pages 121–126. IEEE Computer Society, Los Alamitos, CA, USA, 2000.

    Google Scholar 

  70. P. Dell’Olmo, S. Giordani, and M.G. Speranza. An approximation result for duo-processor task scheduling problem. Information Processing Letters, 61(4):195–200, 1997.

    MathSciNet  Google Scholar 

  71. P. Dell’Olmo, M.G. Speranza, and Z. Tuza. Comparability graph augmentation for some multipocessor scheduling problems. Discrete Applied Mathematics, 72(1–2), 1997.

    Google Scholar 

  72. P. Dell’Olmo, M.G. Speranza, and Z. Tuza. Efficiency and effectiveness of normal schedules on three dedicated processors. Discrete Mathematics, 164(1–3), 1997.

    Google Scholar 

  73. X. Deng, N. Gu, T. Brecht, and K. Lu. Preemptive scheduling of parallel jobs on multiprocessors. SIAM Journal on Computing, 30(1):145–160, 2000.

    MATH  MathSciNet  Google Scholar 

  74. P. Dharwadkar, H.J. Siegel, and E.K.P. Chong. A heuristic for dynamic bandwidth allocation with preemption and degradation for prioritized requests. In Proceedings of 21st International Conference on Distributed Computing Systems (ICDCS’01), pages 547–556, 2001.

    Google Scholar 

  75. J. Ding and L.N. Bhuyan. An adaptive submesh allocation strategy for two-dimensional mesh connected systems. In Proceedings of the International Conference on Parallel Processing (ICPP’93), pages 193–200. IEEE Computer Society, Los Alamitos, CA, USA, 1993.

    Google Scholar 

  76. G. Dobson and U.S. Karmarkar. Simultaneous resource scheduling to minimize weighted flow times. Operations Research, 37(4):592–600, 1989.

    MATH  MathSciNet  Google Scholar 

  77. M. Drabowski. Szeregowanie zadań w systemach wielomikroprocesorowych. Ph.D. thesis, Poznań University of Technology, 1985.

    Google Scholar 

  78. M. Drozdowski. Scheduling multiprocessor tasks on hypercubes. Bulletin of the Polish Academy of Sciences, Technical Sciences, 42(3):437–445, 1994.

    MATH  Google Scholar 

  79. M. Drozdowski. On complexity of multiprocessor tasks scheduling. Bulletin of the Polish Academy of Sciences, Technical Sciences, 43(3):381–392, 1995.

    MATH  Google Scholar 

  80. M. Drozdowski. Real-time scheduling of linear speedup parallel tasks. Information Processing Letters, 57(1):35–40, 1996.

    MATH  Google Scholar 

  81. M. Drozdowski. Scheduling multiprocessor tasks – an overview. European Journal of Operational Research, 94:215–230, 1996.

    MATH  Google Scholar 

  82. M. Drozdowski. Selected Problems of Scheduling Tasks in Multiprocessor Computer Systems. Number 321 in Monographs. Poznań University of Technology Press, Poznań, 1997. http://www.cs.put.poznan.pl/~maciejd/txt/h.ps.

  83. M. Drozdowski. New applications of the Munz and Coffman algorithm. Journal of Scheduling, 4(4):209–223, 2001.

    MATH  MathSciNet  Google Scholar 

  84. M. Drozdowski and P. Dell’Olmo. Scheduling multiprocessor tasks for mean flow time criterion. Computers and Operations Research, 27(6):571–585, 2000.

    MATH  MathSciNet  Google Scholar 

  85. M. Drozdowski and W. Kubiak. Scheduling parallel tasks with sequential heads and tails. Annals of Operations Research, 90:221–246, 1999.

    MATH  MathSciNet  Google Scholar 

  86. J. Du and J.Y-T. Leung. Complexity of scheduling parallel task systems. SIAM Journal on Discrete Mathematics, 2(4):472–478, 1989.

    Google Scholar 

  87. P.F. Dutot, G. Mounié, and D. Trystram. Scheduling parallel tasks: Approximation algorithms. In J.Y. Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pages 26.1–26.24. CRC Press, Boca Raton, 2004.

    Google Scholar 

  88. S. Dutt and J. P. Hayes. Subcube allocation in hypercube computers. IEEE Transactions on Computers, 40(3):341–352, 1991.

    MathSciNet  Google Scholar 

  89. J. Edmonds. Scheduling in the dark. Theoretical Computer Science, 235(1):109–141, 2000.

    MATH  MathSciNet  Google Scholar 

  90. J. Edmonds, D. Chinn, T. Brecht, and X. Deng. Non-clairvoyant multiprocessor scheduling of jobs with changing execution characteristics. Journal of Scheduling, 6(3):231–250, 2003.

    MATH  MathSciNet  Google Scholar 

  91. K. Efe and V. Krishnamoorthy. Optimal scheduling of compute-intensive tasks on a network of workstations. IEEE Transactions on Parallel and Distributed Systems, 6(6):668–673, 1995.

    Google Scholar 

  92. D.G. Feitelson. Workshops on job scheduling strategies for parallel processing. http://www.cs.huji.ac.il/~feit/parsched/ [online accessed 25 August 2007].

  93. D.G. Feitelson. Packing schemes for gang scheduling. In D.G. Feitelson and L. Rudolph, editors, Proceedings of 2nd Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 1162, pages 89–110. Springer, Berlin, 1996.

    Google Scholar 

  94. D.G. Feitelson. Memory usage in the LANL CM-5 workload. In D.G. Feitelson and L. Rudolph, editors, Proceedings of 3rd Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 1291, pages 78–94. Springer, Berlin, 1997.

    Google Scholar 

  95. D.G. Feitelson. Parallel workloads archive. http://www.cs.huji.ac.il/labs/parallel/workload/, 2007 [online accessed 20 May 2007].

  96. D.G. Feitelson. Workload Modeling for Computer Systems Performance Evaluation. 2007. Version 0.10, http://www.cs.huji.ac.il/~feit/wlmod/wlmod.pdf [online accessed 20 May 2007].

  97. D.G. Feitelson and L. Rudolph. Distributed hierarchical control for parallel processing. IEEE Computer, 23(5):65–77, 1990.

    Google Scholar 

  98. D.G. Feitelson and L. Rudolph. Evaluation of design choices for gang scheduling using distributed hierarchical control. Journal of Parallel and Distributed Computing, 35(1):18–34, 1996.

    MATH  Google Scholar 

  99. D.G. Feitelson and L. Rudolph. Metrics and benchmarking for parallel job scheduling. In D.G. Feitelson and L. Rudolph, editors, Job Scheduling Strategies for Parallel Processing. LNCS, volume 1459, pages 1–24. Springer, Berlin, 1998.

    Google Scholar 

  100. D.G. Feitelson, L. Rudolph, U. Schwiegelshohn, K. Sevcik, and P. Wong. Theory and practice in parallel job scheduling. In D.G. Feitelson and L. Rudolph, editors, Job Scheduling Strategies for Parallel Processing. LNCS, volume 1291, pages 1–34. Springer, Berlin, 1997.

    Google Scholar 

  101. D.G. Feitelson and A. Mu’alem Weil. Utilization and predictability in scheduling the IBM SP2 with backfilling. In Proceedings of 12th International Parallel Processing Symposium, pages 542–546. IEEE Computer Society, Los Alamitos, CA, USA, 1998.

    Google Scholar 

  102. A. Feldmann, M.-Y. Kao, J. Sgall, and S.-H. Teng. Optimal online scheduling of parallel jobs with dependencies. Journal of Combinatorial Optimization, 1(4):393–411, 1998.

    MATH  MathSciNet  Google Scholar 

  103. A. Feldmann, J. Sgall, and S.-H. Teng. Dynamic scheduling on parallel machines. Theoretical Computer Science, 130(1):49–72, 1994.

    MATH  MathSciNet  Google Scholar 

  104. W. Feng and J. Rexford. Performance evaluation of smoothing algorithms for transmitting prerecorded variable-bit-rate video. IEEE Transactions on Multimedia, 1(3):302–313, 1999.

    Google Scholar 

  105. A. Fishkin, K. Jansen, and L. Porkolab. On minimizing average weighted completion time: A PTAS for scheduling general multiprocessor tasks. In R. Freivalds, editor, Proceedings of 13th International Symposium on Fundamentals of Computation Theory (FCT’01). LNCS, volume 2138, pages 495–507, 2001.

    Google Scholar 

  106. A. Fishkin, K. Jansen, and L. Porkolab. On minimizing average weighted completion time of multiprocessor tasks with release dates. In F. Orejas, P.G. Spirakis, and J. van Leeuwen, editors, Proceedings of 28th International Colloquium on Automata, Languages and Programming (ICALP’01). LNCS, volume 2076, pages 875–886, 2001.

    Google Scholar 

  107. A.V. Fishkin and G. Zhang. On maximizing throughput of multiprocessor tasks. In K. Diks and W. Ritter, editors, Proceedings of 27th International Symposium Mathematical Foundations of Computer Science (MFCS’02). LNCS, volume 2420, pages 269–279. Springer, Berlin, 2002.

    Google Scholar 

  108. C. Flaviu. Understanding fault-tolerant distributed systems. Communications of the ACM, 34(2):56–78, 1991.

    Google Scholar 

  109. E. Frachtenberg, D.G. Feitelson, F. Petrini, and J. Fernandez. Adaptive parallel job scheduling with flexible coscheduling. IEEE Transactions on Parallel and Distributed Systems, 16(11):1066–1077, 2005.

    Google Scholar 

  110. M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  111. E.F. Gehringer, D.P. Siewiorek, and Z. Segall. Parallel Processing: The Cm ∗ Experience. Digital Press, Bedford, 1987.

    Google Scholar 

  112. D. Ghosal, G. Serazzi, and S. Tripathi. The processor working set and its use in scheduling multiprocessor systems. IEEE Transactions on Software Engineering, 17(5):443–453, 1991.

    Google Scholar 

  113. K. Giaro, M. Kubale, M. Małafiejski, and K. Piwakowski. Chromatic scheduling of dedicated 2-processor UET tasks to minimize mean flow time. In Proceedings of 7th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA’99), pages 343–347, 1999.

    Google Scholar 

  114. K. Giaro, M. Kubale, M. Małafiejski, and K. Piwakowski. Dedicated scheduling of biprocessor tasks to minimize mean flow time. In R. Wyrzykowski et al., editor, Proceedings of 4th International Conference on Parallel Processing and Applied Mathematics (PPAM’01). LNCS, volume 2328, pages 87–96. Springer, 2000.

    Google Scholar 

  115. J. Glasgow and H. Shachnai. Channel based scheduling of parallelizable tasks. In Proceedings of 5th IEEE International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems (MASCOTS’97), pages 11–16. IEEE Computer Society, Los Alamitos, CA, USA, 1997.

    Google Scholar 

  116. M.X. Goemans. An approximation algorithm for scheduling on three dedicated processors. Discrete Applied Mathematics, 61(1):49–59, 1995.

    MATH  MathSciNet  Google Scholar 

  117. V. Gupta and A. Jayendran. A flexible processor allocation strategy for mesh connected parallel systems. In Proceedings of 1996 International Conference on Parallel Processing (ICPP’96), pages III.166–III.173, 1996.

    Google Scholar 

  118. H.-J. Ho and W.-M. Lin. A performance-optimizing technique for mesh-connected multicomputers based on real-time job size distribution. In Proceedings of 10th International Conference on Parallel and Distributed Systems (ICPADS’04), pages 639–646, 2004.

    Google Scholar 

  119. C.P.M. van Hoesel. Preemptive scheduling on a hypercube. Technical Report 8963/A, Erasmus University, Rotterdam, The Netherlands, 1989.

    Google Scholar 

  120. I. Holyer. The NP-completeness of edge-coloring. SIAM Journal on Computing, 10(4):718–720, 1981.

    MATH  MathSciNet  Google Scholar 

  121. J.A. Hoogeveen, S.L. van de Velde, and B. Veltman. Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discrete Applied Mathematics, 55(3):259–272, 1994.

    MATH  MathSciNet  Google Scholar 

  122. A. Hori, Y. Ishikawa, H. Konaka, M. Maeda, and T. Tomokiyo. A scalable time-sharing scheduling for partitionable distributed memory parallel machines. In Proceedings of 28th Hawaii International Conference on System Sciences (HICSS’95), pages 173–182, 1995.

    Google Scholar 

  123. J. Huang, J. Chen, and S. Chen. A simple linear-time approximation algorithm for multi-processor job scheduling on four processors. In D.T. Lee and S.-H. Teng, editors, Proceedings of 11th International Symposium Algorithms and Computation (ISAAC’00). LNCS, volume 1969, pages 60–71, 2000.

    Google Scholar 

  124. J. Hungershofer. On the combined scheduling of malleable and rigid jobs. In Proceedings of 16th Symposium on Computer Architecture and High Performance Computing (SBAC-PAD’04), pages 206–213. IEEE Computer Society, Los Alamitos, CA, USA, 2004.

    Google Scholar 

  125. I. Hwang. An efficient processor allocation algorithm using two-dimensional packing. Journal of Parallel and Distributed Computing, 42(1), 1997.

    Google Scholar 

  126. A. Iovanella. On-line algorithms for multiprocessor task scheduling. Ph.D. thesis, Universitá degli Studi di Roma “La Sapienza”, 2002.

    Google Scholar 

  127. D. Jackson, Q. Snell, and M. Clement. Core algorithms of the Maui scheduler. In D. Feitelson and L. Rudolph, editors, Proceedings of 7th Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 2221, pages 87–102, Springer, Berlin, 2001.

    Google Scholar 

  128. K. Jansen. Scheduling malleable parallel tasks: An asymptotic fully polynomial-time approximation scheme. In R. Möhring and R. Raman, editors, Proceedings of ESA 2002. LNCS, volume 2461, pages 562–574, Berlin, 2002. Springer.

    Google Scholar 

  129. K. Jansen and L. Porkolab. Preemptive parallel task scheduling in o(n) + poly(m) time. In D.T. Lee and S.H. Teng, editors, Proceedings of ISAAC 2000. LNCS, volume 1969, pages 398–409, Springer, Berlin, 2000.

    Google Scholar 

  130. K. Jansen and L. Porkolab. Linear-time approximation schemes for scheduling malleable parallel tasks. Algorithmica, 32(3):507–520, 2002.

    MATH  MathSciNet  Google Scholar 

  131. K. Jansen and L. Porkolab. Polynomial time approximation schemes for general multiprocessor job shop scheduling. Journal of Algorithms, 45(2):167–191, 2002.

    MATH  MathSciNet  Google Scholar 

  132. K. Jansen and L. Porkolab. Computing optimal preemptive schedules for parallel tasks: Linear programming approaches. Mathematical Programming, 95(3):617–630, 2003.

    MATH  MathSciNet  Google Scholar 

  133. K. Jansen and L. Porkolab. Preemptive scheduling on dedicated processors: Applications of fractional graph coloring. Journal of Scheduling, 7(1):35–48, 2004.

    MathSciNet  Google Scholar 

  134. K. Jansen and L. Porkolab. General multiprocessor task scheduling: Approximate solutions in linear time. SIAM Journal on Computing, 35(3):519–530, 2005.

    MATH  MathSciNet  Google Scholar 

  135. K. Jansen and L. Porkolab. On preemptive resource constrained scheduling: Polynomial-time approximation schemes. SIAM Journal on Discrete Mathematics, 20(3):545–563, 2006.

    MATH  MathSciNet  Google Scholar 

  136. K. Jansen and H. Zhang. An approximation algorithm for scheduling malleable tasks under general precedence constraints. ACM Transactions on Algorithms, 2(3):416–434, 2006.

    MathSciNet  Google Scholar 

  137. M. Jeng and H.J. Siegel. A distributed management scheme for partitionable parallel computers. IEEE Transactions on Parallel and Distributed Systems, 1(1):120–126, 1990.

    Google Scholar 

  138. P. Jędrzejowicz and I. Wierzbowska. Scheduling multiple variant programs under hard real-time constraints. European Journal of Operational Research, 127:458–465, 2000.

    MATH  Google Scholar 

  139. B. Johannes. Scheduling parallel jobs to minimize the makespan. Journal of Scheduling, 9(5):433–452, 2006.

    MATH  MathSciNet  Google Scholar 

  140. J. Józefowska and J. Węglarz. Scheduling with resource constraints – continuous resources. In J.Y. Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pages 24.1–24.15. CRC Press, Boca Raton, 2004.

    Google Scholar 

  141. B. Kalyanasundaram and K. Pruhs. Dynamic spectrum allocation: The impotency of duration notification. Journal of Scheduling, 3(5):289–295, 2000.

    MATH  MathSciNet  Google Scholar 

  142. P.J. Keleher, D. Zotkin, and D. Perkovic. Attacking the bottlenecks of backfilling schedulers. Cluster Computing, 3(4):245–254, 2000.

    Google Scholar 

  143. J. Kim, C.R. Das, and W. Lin. A top-down processor allocation scheme for hypercube computers. IEEE Transactions on Parallel and Distributed Systems, 2(1):20–30, 1991.

    Google Scholar 

  144. D.E. Knuth. The Art of Computer Programming. Volume 1. Fundamental Algorithms. Addison-Wesley Reading MA, Third Edition, 1997.

    Google Scholar 

  145. H. Kopetz and P. Veríssimo. Real time and dependability concepts. In S. Mullender, editor, Distributed Systems, pages 411–446. Addison-Wesley and ACM Press, New York, 1994.

    Google Scholar 

  146. Y. Kopidakis and V. Zissimopoulos. An approximation scheme for scheduling independent jobs into subcubes of a hypercube of fixed dimension. Theoretical Computer Science, 178(1–2):265–273, 1997.

    MATH  MathSciNet  Google Scholar 

  147. E. Koukis and N. Koziris. Memory bandwidth aware scheduling for SMP cluster nodes. In Proceedings of 13th Euromicro Conference on Parallel, Distributed and Network-Based Processing (Euromicro-PDP’05), pages 187–196. IEEE Computer Society, Los Alamitos, CA, USA, 2005.

    Google Scholar 

  148. H. Krawczyk and M. Kubale. An approximation algorithm for diagnostic test scheduling in multicomputer systems. IEEE Transactions on Computers, 34(9):869–872, 1985.

    Google Scholar 

  149. R. Krishnamurti and D.R. Gaur. An approximation algorithm for nonpreemptive scheduling on hypercube parallel task systems. Information Processing Letters, 72(5–6):183–188, 1999.

    MATH  MathSciNet  Google Scholar 

  150. R. Krishnamurti and E. Ma. An approximation algorithm for scheduling tasks on varying partition sizes in partitionable, multiprocessor systems. IEEE Transactions on Computers, 41(12):1572–1579, 1992.

    Google Scholar 

  151. R. Krishnamurti and B. Narahari. An approximation algorithm for preemptive scheduling on parallel-task systems. SIAM Journal on Discrete Mathematics, 8(4):661–669, 1995.

    MATH  MathSciNet  Google Scholar 

  152. P. Krueger and D. Babbar. The effects of precedence and priority constraints on the performance of scan scheduling for hypercube multiprocessors. Journal of Parallel and Distributed Computing, 39(2):95–104, 1996.

    Google Scholar 

  153. P. Krueger, T.-H. Lai, and V.A. Dixit-Radiya. Job scheduling is more important than processor allocation for hypercube computers. IEEE Transaction on Parallel and Distributed Sysytems, 5(5):488–497, 1994.

    Google Scholar 

  154. M. Kubale. The complexity of scheduling independent two-processor tasks on dedicated processors. Information Processing Letters, 24(3):141–147, 1987.

    MATH  MathSciNet  Google Scholar 

  155. M. Kubale. Podzielne uszeregowania zadań dwuprocesorowych na procesorach dedykowanych. Zeszyty Naukowe Politechniki Śląskiej, Seria:Automatyka z.100, Nr kol. 1082, pages 145–153, 1990.

    Google Scholar 

  156. M. Kubale. Preemptive versus nonpreemtive scheduling of biprocessor tasks on dedicated processors. European Journal of Operational Research, 94(2):242–251, 1996.

    MATH  Google Scholar 

  157. M. Kubale, editor. Graph Colorings. American Mathematical Society, Providence, RI, 2004.

    MATH  Google Scholar 

  158. O.-H. Kwon and K.-Y. Chwa. An algorithm for scheduling jobs in hypercube systems. IEEE Transactions on Parallel and Distributed Systems, 9(9):856–860, 1998.

    Google Scholar 

  159. O.-H. Kwon and K.-Y. Chwa. Scheduling parallel tasks with individual deadlines. Theoretical Computer Science, 215(1-2):209–223, 1999.

    MATH  MathSciNet  Google Scholar 

  160. J. Labetoulle, E.L. Lawler, J.K. Lenstra, and Alexander H.G. Rinnoy Kan. Preemptive scheduling of uniform machines subject to release dates. In W.R. Pulleyblank, editor, Progress in Combinatorial Optimization, pages 245–261. Academic, New York, 1984.

    Google Scholar 

  161. C.-Y. Lee and X. Cai. Scheduling one and two-processor tasks on two parallel processors. IEE Transactions, 31(5):445–455, 1999.

    Google Scholar 

  162. W.Y. Lee, S.J. Hong, and J. Kim. On-line scheduling of scalable real-time tasks on multiprocessor systems. Journal of Parallel and Distributed Computing, 63(12):1315–1324, 2003.

    MATH  Google Scholar 

  163. A. Legrand, A. Su, and F. Vivien. Minimizing the stretch when scheduling flows of divisible requests. Technical Report No 2006-19, Laboratoire de l’Informatique du Parallélisme, École Normale Supérieure de Lyon, 2006. Research Report.

    Google Scholar 

  164. R. Lepére, D. Trystram, and G. Woeginger. Approximation algorithms for scheduling malleable tasks under precedence constraints. International Journal of Foundations of Computer Science, 13(4):613–627, 2002.

    MATH  MathSciNet  Google Scholar 

  165. V.J. Leung, E.M. Arkin, M.A. Bender, D. Bunde, J. Johnston, A. Lal, J.S.B. Mitchell, C. Phillips, and S. Seiden. Processor allocation on Cplant: Achieving general processor locality using one-dimensional allocation strategies. In Proceedings of the IEEE International Conference on Cluster Computing (CLUSTER’02), pages 296–304, 2002.

    Google Scholar 

  166. S.T. Leutenegger and M.K. Vernon. The performance of multiprogrammed multiprocessor scheduling policies. In Proceedings of the 1990 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, pages 226–236, 1990.

    Google Scholar 

  167. K. Li. Analysis of an approximation algorithm for scheduling independent parallel tasks. Discrete Mathematics and Theoretical Computer Science, 3(4):155–166, 1999.

    MATH  MathSciNet  Google Scholar 

  168. K. Li. Analysis of the list scheduling algorithm for precedence constrained parallel tasks. Journal of Combinatorial Optimization, 3(1):73–88, 1999.

    MATH  MathSciNet  Google Scholar 

  169. K. Li and K.-H. Cheng. Static job scheduling in partitionable mesh connected systems. Journal of Parallel and Distributed Computing, 10(2):152–159, 1990.

    Google Scholar 

  170. K. Li and K.-H. Cheng. Job scheduling in a partitionable mesh using a two-dimensional buddy system partitioning scheme. IEEE Transactions on Parallel and Distributed Systems, 2(4):413–423, 1991.

    Google Scholar 

  171. K. Li and K.-H. Cheng. A two-dimensional buddy system for dynamic resource allocation in a partitionable mesh connected system. Journal of Parallel and Distributed Computing, 12(1):79–83, 1991.

    MathSciNet  Google Scholar 

  172. K. Li and Y. Pan. Probabilistic analysis of scheduling precedence constrained parallel tasks on multicomputers with contiguous processor allocation. IEEE Transactions on Computers, 49(10):1021–1030, 2000.

    MathSciNet  Google Scholar 

  173. D.A. Lifka. The ANL/IBM SP scheduling system. In D. Feitelson and L. Rudolph, editors, Proceedings of 1st Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 949, pages 295–303, Springer, Berlin, 1995.

    Google Scholar 

  174. J.-F. Lin and S.-J. Chen. Scheduling algorithm for nonpreemptive multiprocessor tasks. Computers and Mathematics with Applications, 28(4):85–92, 1994.

    MathSciNet  Google Scholar 

  175. E.L. Lloyd. Concurrent task systems. Operations Research, 29(1):189–201, 1981.

    MATH  MathSciNet  Google Scholar 

  176. V. Lo, K.J. Windisch, W. Liu, and B. Nitzberg. Noncontiguous processor allocation algorithms for mesh-connected multicomputers. IEEE Transactions on Parallel and Distributed Systems, 8(7):712–726, 1997.

    Google Scholar 

  177. A. Lodi, S. Martello, and M. Monaci. Two-dimensional packing problems: A survey. European Journal of Operational Research, 141(2):241–252, 2002.

    MATH  MathSciNet  Google Scholar 

  178. U. Lublin and D.G. Feitelson. The workload on parallel supercomputers: Modeling the characteristics of rigid jobs. Journal of Parallel and Distributed Computing, 63(11):1105–1122, 2003.

    MATH  Google Scholar 

  179. J. Mache and V. Lo. The effects of dispersal on message-passing contention in processor allocation strategies. In Proceedings of 3rd Joint Conference on Information Sciences, volume 3, pages 223–226, 1997.

    Google Scholar 

  180. J. Mache, V. Lo, and K. Windisch. Minimizing message-passing contention in fragmentation free processor allocation. In Proceedings of 10th International Conference on Parallel and Distributed Computing Systems, pages 120–124, 1997.

    Google Scholar 

  181. R. Mansini, M.G. Speranza, and Z. Tuza. Scheduling groups of tasks with precedence constraints on three dedicated processors. Discrete Applied Mathematics, 134(1–3):141–168, 2004.

    MATH  MathSciNet  Google Scholar 

  182. C. McCann, R. Vaswani, and J. Zahorjan. A dynamic processor allocation policy for multiprogrammed shared-memory multiprocessors. ACM Transactions on Computer Systems, 11(2):146–178, 1993.

    Google Scholar 

  183. M.P. McGarry, M. Maier, and M. Reisslein. Ethernet PONs: A survey of dynamic bandwidth allocation (DBA) algorithms. IEEE Communications Magazine, 42(8), 2004.

    Google Scholar 

  184. D. Min and M.W. Mutka. Efficient job scheduling in a mesh multicomputer without discrimination against large jobs. In Proceedings of 7th IEEE Symposium on Parallel and Distributed Processing (SPDP ’95), pages 52–59, 1995.

    Google Scholar 

  185. P. Mohapatra. Processor allocation using partitioning in mesh connected parallel computers. Journal of Parallel and Distributed Computing, 39(1):181–190, 1996.

    Google Scholar 

  186. P. Mohapatra. Dynamic real-time task scheduling on hypercubes. Journal of Parallel and Distributed Computing, 46(1):91–100, 1997.

    Google Scholar 

  187. P. Mohapatra, C. Yu, and C. Das. A lazy scheduling scheme for hypercube computers. Journal of Parallel and Distributed Computing, 27(1):26–37, 1995.

    MATH  Google Scholar 

  188. R. Motwani, S. Phillips, and E. Torng. Non-clairvoyant scheduling. Theoretical Computer Science, 130(1):17–47, 1994.

    MATH  MathSciNet  Google Scholar 

  189. G. Mounié, C. Rapine, and D. Trystram. A \(\frac{3} {2}\) approximation algorithm for scheduling independent monotonic malleable tasks. Technical report, ID-IMAG Laboratory, Grenoble, France, 2002. http://www-id.imag.fr/Laboratoire/Membres/Trystram_Denis/publis_malleable/MRT_indepSIAM.pdf [online accessed 10 August 2007].

  190. A.W. Mu’alem and D. G. Feitelson. Utilization, predictability, workloads, and user runtime estimates in scheduling the IBM SP2 with backfilling. IEEE Transactions on Parallel and Distributed Systems, 12(6):529–543, 2001.

    Google Scholar 

  191. V.K. Naik, S.K. Setia, and M.S. Squillante. Processor allocation in multiprogrammed distributed-memory parallel computer systems. Journal of Parallel and Distributed Computing, 47(1):28–47, 1997.

    Google Scholar 

  192. E. Naroska and U. Schwiegelshohn. On an on-line scheduling problem for parallel jobs. Information Processing Letters, 81(6):297–304, 2002.

    MATH  MathSciNet  Google Scholar 

  193. C. Oguz, Y. Zinder, V.H. Do, A. Janiak, and M. Lichtenstein. Hybrid flow-shop scheduling problems with multiprocessor task systems. European Journal of Operational Research, 152(1):115–131, 2004.

    MATH  MathSciNet  Google Scholar 

  194. J. Padhye and L. Dowdy. Dynamic versus adaptive processor allocation policies for message passing parallel computers: An empirical comparison. In D.G. Feitelson and L. Rudolph, editors, Proceedings of 2nd Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 1162, pages 224–243, 1996.

    Google Scholar 

  195. J.L. Peterson and T.A. Norman. Buddy systems. Communications of the ACM, 20(6):421–431, 1977.

    MATH  Google Scholar 

  196. J. Plehn. Preemptive scheduling of independent jobs with release times and deadlines on a hypercube. Information Processing Letters, 34(3):161–166, 1990.

    MATH  MathSciNet  Google Scholar 

  197. G.N.S. Prasanna, A. Agarwal, and B.R. Musicus. Hierarchical compilation of macro dataflow graphs for multiprocessors with local memory. IEEE Transactions on Parallel and Distributed Systems, 5(7):720–736, 1994.

    Google Scholar 

  198. G.N.S. Prasanna and B.R. Musicus. Generalized multiprocessor scheduling using optimal control. In Proceedings of 3rd Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA’91), pages 216–228, 1991.

    Google Scholar 

  199. S.G.N. Prasanna and B.R. Musicus. Generalized multiprocessor scheduling for directed acyclic graphs. In Proceedings of Supercomputing 1994, pages 237–246. IEEE Computer Society, Los Alamitos, CA, USA, 1994.

    Google Scholar 

  200. S.G.N. Prasanna and B.R. Musicus. Generalized multiprocessor scheduling and applications to matrix computations. IEEE Transactions on Parallel and Distributed Systems, 7(6):650 – 664, 1996.

    Google Scholar 

  201. W. Qiao and L.M. Ni. Efficient processor allocation for 3D tori. In Proceedings of 9th International Parallel Processing Symposium (IPPS ’95), pages 466–471, 1995.

    Google Scholar 

  202. S. Rai, J.L. Trahan, and T. Smailus. Processor allocation in hypercube multiprocessors. IEEE Transactions on Parallel and Distributed Systems, 6(6):606–616, 1995.

    Google Scholar 

  203. E. Rosti, E. Smirni, L.W. Dowdy, G. Serazzi, and B.M. Carlson. Robust partitioning policies of multiprocessor systems. Performance Evaluation, 19:141–165, 1994.

    Google Scholar 

  204. S. Sahni. Algorithms for scheduling independent tasks. Journal of the ACM, 23(1):116–127, 1976.

    MATH  MathSciNet  Google Scholar 

  205. U. Schwiegelshohn, W. Ludwig, J.L. Wolf, J. Turek, and P.S. Yu. Smart SMART bounds for weighted response time scheduling. SIAM Journal on Computing, 28:237–253, 1998.

    MATH  MathSciNet  Google Scholar 

  206. K.-H. Seo and S.-C. Kim. Extended flexible processor allocation strategy for mesh-connected systems using shape manipulations. In Proceedings of International Conference on Parallel and Distributed Systems, pages 780–787, 1997.

    Google Scholar 

  207. S.K. Setia, M.S. Squillante, and S.K. Tripathi. Analysis of processor allocation in multiprogrammed, distributed-memory parallel processing systems. IEEE Transactions on Parallel and Distributed Systems, 5(4):401–420, 1994.

    Google Scholar 

  208. J. Sgall. Randomized on-line scheduling of parallel jobs. Journal od Algorithms, 21(1):149–175, 1996.

    MATH  MathSciNet  Google Scholar 

  209. D.D. Sharma and D.K. Pradhan. A novel approach for subcube allocation in hypercube multiprocessors. In Proceedings of 4th IEEE Symposium on Parallel and Distributed Processing, pages 336–345, 1992.

    Google Scholar 

  210. D.D. Sharma and D.K. Pradhan. Submesh allocation in mesh multicomputers using busy-list: A best-fit approach with complete recognition capability. Journal of Parallel and Distributed Computing, 36(2):106–118, 1996.

    Google Scholar 

  211. D.D. Sharma and D.K. Pradhan. Job scheduling in mesh multicomputers. IEEE Transactions on Parallel and Distributed Systems, 9(1):57–70, 1998.

    Google Scholar 

  212. X. Shen and E.M. Reingold. Scheduling on a hypercube. Information Processing Letters, 40(6):323–328, 1991.

    MATH  Google Scholar 

  213. D.P. Siewiorek. Fault tolerance in commercial computers. IEEE Computer, pages 26–37, 1990.

    Google Scholar 

  214. A. Silberschatz, J.L. Peterson, and P.B. Galvin. Operating Systems Concepts. Addison-Wesley, Reading MA, USA, 1991.

    Google Scholar 

  215. F. Sivrikaya-Serifoglu and G. Ulusoy. Multiprocessor task scheduling in multistage hybrid flow-shops: A genetic algorithm approach. Journal of the Operational Research Society, 55(5):504–512, 2004.

    MATH  Google Scholar 

  216. J. Skovira, W. Chan, H. Zhou, and D. Lifka. The EASY – LoadLeveler API project. In D. Feitelson and L. Rudolph, editors, Proceedings of 2nd Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 1162, pages 41–47, Springer, Berlin, 1996.

    Google Scholar 

  217. M.S. Squillante. On the benefits and limitations of dynamic partitioning in the parallel computer systems. In D.G. Feitelson and L. Rudolph, editors, Proceedings of 1st Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 949, pages 219–238, 1995.

    Google Scholar 

  218. S. Srinivasan, V. Subramani, R. Kettimuthu, P. Holenarsipur, and P. Sadayappan. Effective selection of partition sizes for moldable scheduling of parallel jobs. In S. Sahni, V.K. Prasanna, and U. Shukla, editors, Proceedings of 9th International Conference on High Performance Computing (HiPC’02). LNCS, volume 2552, pages 174–183, 2002.

    Google Scholar 

  219. A. Steinberg. A strip-packing algorithm with absolute performance bound 2. SIAM Journal on Computing, 26(2):401–409, 1997.

    MATH  MathSciNet  Google Scholar 

  220. D. Talby and D.G. Feitelson. Supporting priorities and improving utilization of the IBM SP scheduler using slack-based backfilling. In Proceedings of 13th International Parallel Processing Symposium, pages 513–517. IEEE, 1999.

    Google Scholar 

  221. A.S. Tanenbaum. Modern Operating Systems. Prentice-Hall, Upper Saddle River NJ, 2001.

    Google Scholar 

  222. A. Tucker and A. Gupta. Process control and scheduling issues for multiprogrammed shared-memory multiprocessors. In Proceedings of 12th ACM Symposium on Operating System Principles, pages 159–166, 1989.

    Google Scholar 

  223. J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In Proceedings of 6th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA’94), pages 200–209. ACM, New York, NY, USA, 1994.

    Google Scholar 

  224. J. Turek, U. Schwiegelshohn, J.L. Wolf, and P.S. Yu. Scheduling parallel tasks to minimize average response time. In Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete algorithms (SODA’94), pages 112–121. SIAM, Philadelphia PA, USA, 1994.

    Google Scholar 

  225. J. Turek, J.L. Wolf, K.R. Pattipati, and P.S. Yu. Scheduling parallelizable tasks: Putting it all on the shelf. ACM SIGMETRICS Performance Evaluation Review, 20(1):225–236, 1992.

    Google Scholar 

  226. J. Turek, J.L. Wolf, and P. S. Yu. Approximate algorithms for scheduling parallelizable tasks. In Proceedings of 4th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA’92), pages 323–332. ACM, New York, NY, USA, 1992.

    Google Scholar 

  227. B. Veltman, B.J. Lageweg, and J.K. Lenstra. Multiprocessor scheduling with communications delays. Parallel Computing, 16:173–182, 1990.

    MATH  Google Scholar 

  228. V.G. Vizing. About schedules observing dead-lines (in Russian). Kibernetika, (1):128–135, 1981.

    Google Scholar 

  229. V.G. Vizing. Minimization of the maximum delay in servicing systems with interruption. U.S.S.R. Computatioanl Mathematics and Mathematical Physics, 22(3):227–233, 1982.

    Google Scholar 

  230. Q. Wang and K.-H. Cheng. List scheduling of parallel tasks. Information Processing Letters, 37(5):291–297, 1991.

    MATH  MathSciNet  Google Scholar 

  231. Q. Wang and K.-H. Cheng. A heuristic of scheduling parallel tasks and its analysis. SIAM Journal on Computing, 21(2):281–294, 1992.

    MATH  MathSciNet  Google Scholar 

  232. J.B. Weissman, L.R. Abburi, and D. England. Integrated scheduling: The best of both worlds. Journal of Parallel and Distributed Computing, 63(6):649–668, 2003.

    MATH  Google Scholar 

  233. J. Wêglarz. Modelling and control of dynamic resource allocation project scheduling systems. In S.G. Tzafestas, editor, Optimization and Control of Dynamic Operational Research Models, pages 105–140. North-Holland, Amsterdam, 1982.

    Google Scholar 

  234. J. Wêglarz. Scheduling under continuous performing speed vs. resource amount activity models. In R. Słowiński and J. Węglarz, editors, Advances in Project Scheduling, pages 273–295. Elsevier Science, Amsterdam, 1989.

    Google Scholar 

  235. P.R. Wilson, M.S. Johnstone, M. Neely, and David Boles. Dynamic storage allocation: A survey and critical review. In H.G. Baker, editor, Proceedings of International Workshop on Memory Management (IWMM’95). LNCS, volume 986, pages 1–116, 1995.

    Google Scholar 

  236. Y. Wiseman and D.G. Feitelson. Paired gang scheduling. IEEE Transactions on Parallel and Distributed Systems, 14(6), 2003.

    Google Scholar 

  237. J.L. Wolf, J. Turek, M.-S. Chen, and P.S. Yu. A hierarchical approach to parallel multiquery scheduling. IEEE Transactions on Parallel and Distributed Systems, 6(6):578–590, 1995.

    Google Scholar 

  238. F. Wu, C.-C. Hsu, and L.-P. Chou. Processor allocation in the mesh multiprocessors using the leapfrog method. IEEE Transactions on Parallel and Distributed Systems, 14(3):276–289, 2003.

    Google Scholar 

  239. W. Xing and J. Zhang. Parallel machine scheduling with splitting jobs. Discrete Applied Mathematics, 103(1-3):259–269, 2000.

    MATH  MathSciNet  Google Scholar 

  240. D. Ye and G. Zhang. On-line scheduling of parallel jobs with dependencies on 2-dimensional mesh. In T. Ibaraki, N. Katoh, and H. Ono, editors, Proceedings of 14th International Symposium Algorithms and Computation (ISAAC’03). LNCS, volume 2906, pages 329–338, 2003.

    Google Scholar 

  241. B.S. Yoo and C.R. Das. A fast and efficient processor allocation scheme for mesh-connected multicomputers. IEEE Transactions on Computers, 51(1):46–60, 2002.

    Google Scholar 

  242. B.S. Yoo, C.R. Das, and C. Yu. Processor management techniques for mesh-connected multiprocessors. In Proceedings of the 24th International Conference on Parallel Processing, pages 105–112, 1995.

    Google Scholar 

  243. S.-M. Yoo and H.Y. Youn. An efficient task allocation scheme for two-dimensional mesh-connected systems. In Proceedings of the 15th International Conference on Distributed Computing Systems, pages 501–508, 1995.

    Google Scholar 

  244. S.-M. Yoo and H.Y. Youn. An on-line scheduling and allocation scheme for real-time tasks in 2D meshes. In Proceedings of the 7th IEEE Symposium on Parallel and Distributed Processing (SPDP’95), pages 630–637, 1995.

    Google Scholar 

  245. B.B. Zhou, R.P. Brent, C.W. Johnson, and D. Walsh. Resource allocation schemes for gang scheduling. In D. G. Feitelson and L. Rudolph, editors, Proceedings of 5th Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 1659, pages 129–143. Springer, Berlin, 1999.

    Google Scholar 

  246. Y. Zhu. Efficient processor allocation strategies for mesh-connected parallel computers. Journal of Parallel and Distributed Computing, 16(4):328–337, 1992.

    MATH  Google Scholar 

  247. Y. Zhu and M. Ahuja. On job scheduling on a hypercube. IEEE Transactions on Parallel and Distributed Systems, 4(1):62–69, 1993.

    Google Scholar 

  248. Y. Zinder and V.H. Do. Scheduling unit execution time tasks on two parallel machines with the criteria of makespan and total completion time. In G. Kendall, E.K. Burke, S. Petrovic, and M. Gendreau, editors, Multidisciplinary Scheduling: Theory and Applications, pages 83–112. Springer, 2005.

    Google Scholar 

  249. Y. Zinder, V.H. Do, and C. Oğuz. Computational complexity of some scheduling problems with multiprocessor tasks. Discrete Optimization, 2(4):391–408, 2005.

    MATH  MathSciNet  Google Scholar 

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  1. Poznan University of Technology Inst. Computing Science, ul. Piotrowo 2, 60-695, Poznan, Poland

    Maciej Drozdowski

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Drozdowski, M. (2009). Parallel Tasks. In: Scheduling for Parallel Processing. Computer Communications and Networks. Springer, London. https://doi.org/10.1007/978-1-84882-310-5_5

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