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- W4316829963 abstract "We consider the problem of minimizing the total processing time of tardy jobs on a single machine. This is a classical scheduling problem, first considered by [Lawler and Moore 1969], that also generalizes the Subset Sum problem. Recently, it was shown that this problem can be solved efficiently by computing $(max,min)$-skewed-convolutions. 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. We further improve the running time of the minimum tardy processing time computation by introducing a job ``bundling'' technique and achieve a $tilde{O}left(P^{2-1/alpha}right)$ running time, where $tilde{O}left(P^alpharight)$ is the running time of a $(max,min)$-skewed-convolution of vectors of size $P$. This results in a $tilde{O}left(P^{7/5}right)$ time algorithm for tardy processing time minimization, an improvement over the previously known $tilde{O}left(P^{5/3}right)$ time algorithm." @default.
- W4316829963 created "2023-01-17" @default.
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- W4316829963 date "2023-01-13" @default.
- W4316829963 modified "2023-09-27" @default.
- W4316829963 title "Quick Minimization of Tardy Processing Time on a Single Machine" @default.
- W4316829963 doi "https://doi.org/10.48550/arxiv.2301.05460" @default.
- W4316829963 hasPublicationYear "2023" @default.
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