# On Minimizing Tardy Processing Time, Max-Min Skewed Convolution, and Triangular Structured ILPs

@article{Klein2022OnMT, title={On Minimizing Tardy Processing Time, Max-Min Skewed Convolution, and Triangular Structured ILPs}, author={Kim-Manuel Klein and Adam Polak and Lars Rohwedder}, journal={ArXiv}, year={2022}, volume={abs/2211.05053} }

The starting point of this paper is the problem of scheduling n jobs with processing times and due dates on a single machine so as to minimize the total processing time of tardy jobs, i.e., 1 | | P p j U j . This problem was identiﬁed by Bringmann et al. (Algo-rithmica 2022) as a natural subquadratic-time special case of the classic 1 | | P w j U j problem, which likely requires time quadratic in the total processing time P , because of a ﬁne-grained lower bound. Bringmann et al. obtain their e…

## One Citation

### Quick Minimization of Tardy Processing Time on a Single Machine

- Computer ScienceArXiv
- 2023

The running time of the resulting algorithm is equivalent, up to logarithmic factors, to the time it takes to compute a ( max, min ) -skewed-convolution of two vectors of integers whose sum is O ( P ) , where P is the sum of the jobs’ processing times.

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