Improved Online Load Balancing with Known Makespan
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10491729" target="_blank" >RIV/00216208:11320/24:10491729 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.10" target="_blank" >https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.10</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.10" target="_blank" >10.4230/LIPIcs.APPROX/RANDOM.2024.10</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Improved Online Load Balancing with Known Makespan
Popis výsledku v původním jazyce
We break the barrier of 3/2 for the problem of online load balancing with known makespan, also known as bin stretching. In this problem, m identical machines and the optimal makespan are given. The load of a machine is the total size of all the jobs assigned to it and the makespan is the maximum load of all the machines. Jobs arrive online and the goal is to assign each job to a machine while staying within a small factor (the competitive ratio) of the optimal makespan. We present an algorithm that maintains a competitive ratio of 139/93 < 1.495 for sufficiently large values of m, improving the previous bound of 3/2. The value 3/2 represents a natural bound for this problem: as long as the online bins are of size at least 3/2 of the offline bin, all items that fit at least two times in an offline bin have two nice properties. They fit three times in an online bin and a single such item can be packed together with an item of any size in an online bin. These properties are now both lost, which means that putting even one job on a wrong machine can leave some job unassigned at the end. It also makes it harder to determine good thresholds for the item types. This was one of the main technical issues in getting below 3/2. The analysis consists of an intricate mixture of size and weight arguments. (C) Martin Böhm, Matej Lieskovský, Sören Schmitt, Jiří Sgall, and Rob van Stee.
Název v anglickém jazyce
Improved Online Load Balancing with Known Makespan
Popis výsledku anglicky
We break the barrier of 3/2 for the problem of online load balancing with known makespan, also known as bin stretching. In this problem, m identical machines and the optimal makespan are given. The load of a machine is the total size of all the jobs assigned to it and the makespan is the maximum load of all the machines. Jobs arrive online and the goal is to assign each job to a machine while staying within a small factor (the competitive ratio) of the optimal makespan. We present an algorithm that maintains a competitive ratio of 139/93 < 1.495 for sufficiently large values of m, improving the previous bound of 3/2. The value 3/2 represents a natural bound for this problem: as long as the online bins are of size at least 3/2 of the offline bin, all items that fit at least two times in an offline bin have two nice properties. They fit three times in an online bin and a single such item can be packed together with an item of any size in an online bin. These properties are now both lost, which means that putting even one job on a wrong machine can leave some job unassigned at the end. It also makes it harder to determine good thresholds for the item types. This was one of the main technical issues in getting below 3/2. The analysis consists of an intricate mixture of size and weight arguments. (C) Martin Böhm, Matej Lieskovský, Sören Schmitt, Jiří Sgall, and Rob van Stee.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
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)
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-348-5
ISSN
1868-8969
e-ISSN
—
Počet stran výsledku
21
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
—