On the power of randomization for job shop scheduling with k-units length tasks
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 189-207.

In the job shop scheduling problem k-units-J m , there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D. The contribution of this paper are the following results; (i) for d=o(D) jobs and every fixed k, the makespan of an optimal schedule is at most D+o(D), which extends the result of [3] for k=1; (ii) a randomized on-line approximation algorithm for k-units-J m is presented. This is the on-line algorithm with the best known competitive ratio against an oblivious adversary for d=o(D) and k>1; (iii) different processing times yield harder instances than identical processing times. There is no 5/3 competitive deterministic on-line algorithm for k-units-J m , whereas the competitive ratio of the randomized on-line algorithm of (ii) still tends to 1 for d=o(D).

DOI : 10.1051/ita:2008024
Classification : 68W20, 68W25
Mots-clés : on-line algorithms, randomization, competitive ratio, scheduling 
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     title = {On the power of randomization for job shop scheduling with $k$-units length tasks},
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Mömke, Tobias. On the power of randomization for job shop scheduling with $k$-units length tasks. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 189-207. doi : 10.1051/ita:2008024. http://archive.numdam.org/articles/10.1051/ita:2008024/

[1] P. Brucker, An efficient algorithm for the job shop problem with two jobs. Computing 40 (1988) 353-359. | MR | Zbl

[2] U. Feige and C. Scheideler, Improved bounds for acyclic job shop scheduling. Combinatorica 22 (2002) 361-399. | MR

[3] J. Hromkovič, K. Steinhöfel and P. Widmayer, Job shop scheduling with unit length tasks: bounds and algorithms. ICTCS '01: Proceedings of the 7th Italian Conference on Theoretical Computer Science. Lect. Notes Comput. Sci. 2202 (2001) 90-106. | MR | Zbl

[4] J. Hromkovič, T. Mömke, K. Steinhöfel and P. Widmayer, Job shop scheduling with unit length tasks: bounds and algorithms. Algorithmic Operations Research 2 (2007) 1-14. | MR

[5] F.A. Leighton, B.M. Maggs and S.B. Rao, Packet routing and job shop scheduling in O(congestion+dilition) steps. Combinatorica 14 (1994) 167-186. | MR | Zbl

[6] F.A. Leighton, B.M. Maggs and A.W. Richa, Fast algorithms for finding O(congestion+dilation) packet routing schedules. Combinatorica 19 (1999) 375-401. | MR | Zbl

[7] J.K. Lenstra and A.H.G. Rinnooy Kan, Computational complexity of discrete optimization problems. Annals of Discrete Mathematics 4 (1979) 121-140. | MR | Zbl

[8] D.P. Willamson, L.A. Hall, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevast'Janov and D.B. Shmoys, Short shop schedules. Operations Research 45 (1997) 288-294. | MR | Zbl

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