no. 2
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://www.numdam.org/articles/10.1051/ita:2008024/

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