Speed-Robust Scheduling Revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10491728" target="_blank" >RIV/00216208:11320/24:10491728 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.8" target="_blank" >https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.8" target="_blank" >10.4230/LIPIcs.APPROX/RANDOM.2024.8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Speed-Robust Scheduling Revisited

Popis výsledku v původním jazyce

Speed-robust scheduling is the following two-stage problem of scheduling n jobs on m uniformly related machines. In the first stage, the algorithm receives the value of m and the processing times of n jobs; it has to partition the jobs into b groups called bags. In the second stage, the machine speeds are revealed and the bags are assigned to the machines, i.e., the algorithm produces a schedule where all the jobs in the same bag are assigned to the same machine. The objective is to minimize the makespan (the length of the schedule). The algorithm is compared to the optimal schedule and it is called ρ-robust, if its makespan is always at most ρ times the optimal one. Our main result is an improved bound for equal-size jobs for b = m. We give an upper bound of 1.6. This improves previous bound of 1.8 and it is almost tight in the light of previous lower bound of 1.58. Second, for infinitesimally small jobs, we give tight upper and lower bounds for the case when b &gt;= m. This generalizes and simplifies the previous bounds for b = m. Finally, we introduce a new special case with relatively small jobs for which we give an algorithm whose robustness is close to that of infinitesimal jobs and thus gives better than 2-robust for a large class of inputs. (C) Josef Minařík and Jiří Sgall.

Název v anglickém jazyce

Speed-Robust Scheduling Revisited

Popis výsledku anglicky

Speed-robust scheduling is the following two-stage problem of scheduling n jobs on m uniformly related machines. In the first stage, the algorithm receives the value of m and the processing times of n jobs; it has to partition the jobs into b groups called bags. In the second stage, the machine speeds are revealed and the bags are assigned to the machines, i.e., the algorithm produces a schedule where all the jobs in the same bag are assigned to the same machine. The objective is to minimize the makespan (the length of the schedule). The algorithm is compared to the optimal schedule and it is called ρ-robust, if its makespan is always at most ρ times the optimal one. Our main result is an improved bound for equal-size jobs for b = m. We give an upper bound of 1.6. This improves previous bound of 1.8 and it is almost tight in the light of previous lower bound of 1.58. Second, for infinitesimally small jobs, we give tight upper and lower bounds for the case when b &gt;= m. This generalizes and simplifies the previous bounds for b = m. Finally, we introduce a new special case with relatively small jobs for which we give an algorithm whose robustness is close to that of infinitesimal jobs and thus gives better than 2-robust for a large class of inputs. (C) Josef Minařík and Jiří Sgall.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA24-10306S" target="_blank" >GA24-10306S: Nové výzvy proudových, online a kombinatorických algoritmů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-348-5

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

20

Strana od-do

—

Název nakladatele

Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Místo vydání

Germany

Místo konání akce

London

Datum konání akce

28. 8. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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