no. 1
Scheduling an interval ordered precedence graph with communication delays and a limited number of processors
RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 1, pp. 73-87.

We consider the scheduling of an interval order precedence graph of unit execution time tasks with communication delays, release dates and deadlines. Tasks must be executed by a set of processors partitioned into K classes; each task requires one processor from a fixed class. The aim of this paper is to study the extension of the Leung-Palem-Pnueli (in short LPP) algorithm to this problem. The main result is to prove that the LPP algorithm can be extended to dedicated processors and monotone communication delays. It is also proved that the problem is NP-complete for two dedicated processors if communication delays are non monotone. Lastly, we show that list scheduling algorithm cannot provide a solution for identical processors.

DOI : 10.1051/ro/2013028
Classification : 90B35
Mots clés : approximation and complexity, combinatorial optimization, scheduling 
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     title = {Scheduling an interval ordered precedence graph with communication delays and a limited number of processors},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Kordon, Alix Munier; Kacem, Fadi; Dupont de Dinechin, Benoît; Finta, Lucian. Scheduling an interval ordered precedence graph with communication delays and a limited number of processors. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 1, pp. 73-87. doi : 10.1051/ro/2013028. http://www.numdam.org/articles/10.1051/ro/2013028/

[1] H.H. Ali and H.H. El.-Rewini, An optimal algorithm for scheduling interval ordered tasks with communication on processors. J. Comput. Syst. Sci. 2 (1995) 301-307. | MR | Zbl

[2] P. Chrétienne and C. Picouleau, Scheduling with communication delays : a survey. in Scheduling Theory and its Applications, edited P. Chrétienne, E.G. Coffman, J.K. Lenstra and Z. Liu. John Wiley Ltd (1995) 65-89. | MR

[3] B. Dupont De Dinechin, Scheduling monotone interval orders on typed task systems. In PLANSIG 2007, 26th Worshop of the UK Planning and Scheduling Special Interest Group (2007) 25-31.

[4] R. Giroudeau, J.-C. Konig, F.K. Moulai and J. Palaysi, Complexity and approximation for precedence constrained scheduling problems with large communication delays. Theor. Comput. Sci. 401 (2008) 107-119. | MR | Zbl

[5] W. Horn, Some simple scheduling algorithms. Naval Research Logistics Quarterly 21 (1974) 177-185. | MR | Zbl

[6] J. Hwang, Y. Chow, F. Anger and C. Lee, Scheduling precedence graphs in systems with interprocessor communication times. SIAM J. Comput. 18 (1989) 244-257. | MR | Zbl

[7] K. Jansen, Analysis of Scheduling Problems with Typed Task Systems. Discrete Appl. Math. 52 (1994) 223-232. | MR | Zbl

[8] A. Leung, K.V. Palem and A. Pnueli, Scheduling Time-Constrained Instructions on Pipelined Processors. ACM Transact. Program. Languages Syst. 23 (2001) 73-103.

[9] K. Palem and B. Simons, Scheduling time-critical instructions on risc machines. ACM Transactions on Programming Languages and Systems 4 (1993) 632-658.

[10] C.H Papadimitriou and M. Yannakakis, Scheduling interval-ordered tasks. SIAM J. Comput. 8 (1979) 405-409. | MR | Zbl

[11] B. Veltman, B.J. Lageweg and J.K. Lenstra, Multiprocessor scheduling with communication delays. Parallel Comput. 16 (1990) 173-182. | Zbl

[12] J. Verriet, The complexity of scheduling typed task systems with and without communication delays. External Report 1998-26, UU-CS (1998).

[13] J. Verriet, Scheduling interval-ordered tasks with non-uniform deadlines subject to non-zero communication delays. Parallel Comput. 25 (1999) 3-21. | MR | Zbl

[14] W. Yu, H. Hoogeveen and J.K. Lenstra, Minimizing makespan in a two-machine flow shop with delays and unit-time operations is np-hard. J. Scheduling 7 (2004) 333-348. | MR | Zbl

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