A note on scheduling with low rank processing times

Lin Chen; Deshi Ye; Guochuan Zhang

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arXiv · 1306.3727

A note on scheduling with low rank processing times

Lin Chen·Deshi Ye·Guochuan Zhang

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Abstract

We consider the classical minimum makespan scheduling problem, where the processing time of job $j$ on machine $i$ is $p_{ij}$, and the matrix $P=(p_{ij})_{m\times n}$ is of a low rank. It is proved in (Bhaskara et al., SODA 2013) that rank 7 scheduling is NP-hard to approximate to a factor of $3/2-ε$, and rank 4 scheduling is APX-hard (NP-hard to approximate within a factor of $1.03-ε$). We improve this result by showing that rank 4 scheduling is already NP-hard to approximate within a factor of $3/2-ε$, and meanwhile rank 3 scheduling is APX-hard.

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Lin Chen, Deshi Ye, Guochuan Zhang. 2013-06-17. A note on scheduling with low rank processing times. https://arxiv.org/abs/1306.3727

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