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On the power of randomization for job shop scheduling with $k$ -units length tasks

Tobias Mömke — 2009

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 $d = o (\sqrt{D})$ 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-...

On the power of randomization for job shop scheduling with -units length tasks

Tobias Mömke — 2008

RAIRO - Theoretical Informatics and Applications

In the job shop scheduling problem -- , there are machines and each machine has an integer processing time of at most time units. Each job consists of a permutation of tasks corresponding to all machines and thus all jobs have an identical dilation . The contribution of this paper are the following results; (i) for $d = o (\sqrt{D})$ jobs and every fixed , the makespan of an optimal schedule is at most , which extends the result of [3] for ; (ii) a randomized on-line approximation...

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On the power of randomization for job shop scheduling with k -units length tasks

On the power of randomization for job shop scheduling with -units length tasks

On the power of randomization for job shop scheduling with $k$ -units length tasks