Minimizing the Weighted Number of Tardy Jobs via (max,1)-Convolutions

Danny Hermelin; Hendrik Molter; Dvir Shabtay

doi:10.1287/ijoc.2022.0307

Minimizing the Weighted Number of Tardy Jobs via (max,1)-Convolutions

Danny Hermelin, Hendrik Molter, Dvir Shabtay

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH).

Original language	English
Pages (from-to)	836-848
Number of pages	13
Journal	INFORMS Journal on Computing
Volume	36
Issue number	3
DOIs	https://doi.org/10.1287/ijoc.2022.0307
State	Published - 1 May 2024

Keywords

conditional lower bounds
pseudo-polynomial algorithms
single machine scheduling
weighted number of tardy jobs

ASJC Scopus subject areas

Software
Information Systems
Computer Science Applications
Management Science and Operations Research

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10.1287/ijoc.2022.0307

Cite this

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title = "Minimizing the Weighted Number of Tardy Jobs via (max,1)-Convolutions",

abstract = "In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60{\textquoteright}s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH).",

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N2 - In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH).

AB - In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH).

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KW - pseudo-polynomial algorithms

KW - single machine scheduling

KW - weighted number of tardy jobs

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ER -

Minimizing the Weighted Number of Tardy Jobs via (max,1)-Convolutions

Abstract

Keywords

ASJC Scopus subject areas

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Findings from Ben-Gurion University of the Negev Broaden Understanding of Computing [Minimizing the Weighted Number of Tardy Jobs Via (Max, Plus )-convolutions]

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Minimizing the Weighted Number of Tardy Jobs via (max,1)-Convolutions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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Fingerprint

Press/Media

Findings from Ben-Gurion University of the Negev Broaden Understanding of Computing [Minimizing the Weighted Number of Tardy Jobs Via (Max, Plus )-convolutions]

Cite this