Online Bin Packing with Advice

• Published in: Algorithmica Vol. 74; no. 1; pp. 507 - 527
• Main Authors: Boyar, Joan, Kamali, Shahin, Larsen, Kim S., López-Ortiz, Alejandro
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-01-2016
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Mathematics of Computing; Theory of Computation; Advice complexity; Bin packing; Online algorithms
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-014-9955-8

We consider the online bin packing problem under the advice complexity model where the “online constraint” is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with
log
n
+
o
(
log
n
)
bits of advice, achieves a competitive ratio of
3
/
2
for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives
2
n
+
o
(
n
)
bits of advice and achieves a competitive ratio of
4
/
3
+
ε
. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.