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… 
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Quick Minimization of Tardy Processing Time on a Single Machine

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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