Colored Bin Packing: Online Algorithms and Lower Bounds

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Colored Bin Packing: Online Algorithms and Lower Bounds

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GA14-10003S" target="_blank" >GA14-10003S: Restricted computations: Algorithms, models, complexity</a><br>

Continuities

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

Publication year

2018

Confidentiality

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

Name of the periodical

Algorithmica

ISSN

0178-4617

e-ISSN

—

Volume of the periodical

80

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

30

Pages from-to

155-184

UT code for WoS article

000419148000008

EID of the result in the Scopus database

2-s2.0-84995739654