Quick Minimization of Tardy Processing Time on a Single Machine
Document Type
Conference Proceeding
Publication Date
1-1-2023
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 the same, up to logarithmic factors, as 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 O~(P2-1/α) running time, where O~(Pα) is the running time of a (max, min ) -skewed-convolution of vectors of size P. This results in a O~(P7/5) time algorithm for tardy processing time minimization, an improvement over the previously known O~(P5/3) time algorithm.
Identifier
85172733877 (Scopus)
ISBN
[9783031389054]
Publication Title
Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics
External Full Text Location
https://doi.org/10.1007/978-3-031-38906-1_42
e-ISSN
16113349
ISSN
03029743
First Page
637
Last Page
643
Volume
14079 LNCS
Grant
UNCE/SCI/004
Fund Ref
National Science Foundation
Recommended Citation
Schieber, Baruch and Sitaraman, Pranav, "Quick Minimization of Tardy Processing Time on a Single Machine" (2023). Faculty Publications. 2114.
https://digitalcommons.njit.edu/fac_pubs/2114