Colored Bin Packing: Online Algorithms and Lower Bounds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10368748" target="_blank" >RIV/00216208:11320/18:10368748 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00453-016-0248-2" target="_blank" >http://dx.doi.org/10.1007/s00453-016-0248-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-016-0248-2" target="_blank" >10.1007/s00453-016-0248-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Colored Bin Packing: Online Algorithms and Lower Bounds

Popis výsledku v původním jazyce

In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most bins and we can force any deterministic online algorithm to use at least bins while the offline optimum is for any value of . In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real the asymptotic competitive ratio of our algorithm is . We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors-the Black and White Bin Packing problem-we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real we show that the Worst Fit algorithm is absolutely -competitive.

Název v anglickém jazyce

Colored Bin Packing: Online Algorithms and Lower Bounds

Popis výsledku anglicky

In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most bins and we can force any deterministic online algorithm to use at least bins while the offline optimum is for any value of . In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real the asymptotic competitive ratio of our algorithm is . We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors-the Black and White Bin Packing problem-we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real we show that the Worst Fit algorithm is absolutely -competitive.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

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/GA14-10003S" target="_blank" >GA14-10003S: Omezené typy výpočtů: algoritmy, modely, složitost</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Algorithmica

ISSN

0178-4617

e-ISSN

—

Svazek periodika

80

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

155-184

Kód UT WoS článku

000419148000008

EID výsledku v databázi Scopus

2-s2.0-84995739654