eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
13:1
13:17
10.4230/LIPIcs.ICALP.2020.13
article
An Optimal Algorithm for Online Multiple Knapsack
Bienkowski, Marcin
1
https://orcid.org/0000-0002-2453-7772
Pacut, Maciej
2
https://orcid.org/0000-0002-6379-1490
Piecuch, Krzysztof
1
Institute of Computer Science, University of Wrocław, Poland
Faculty of Computer Science, University of Vienna, Austria
In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of n bins (knapsacks) of equal size. The gain of an algorithm is equal to the sum of sizes of accepted items and the goal is to maximize the total gain.
So far, for this natural problem, the best solution was the 0.5-competitive algorithm FirstFit (the result holds for any n ≥ 2). We present the first algorithm that beats this ratio, achieving the competitive ratio of 1/(1+ln(2))-O(1/n) ≈ 0.5906 - O(1/n). Our algorithm is deterministic and optimal up to lower-order terms, as the upper bound of 1/(1+ln(2)) for randomized solutions was given previously by Cygan et al. [TOCS 2016].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.13/LIPIcs.ICALP.2020.13.pdf
online knapsack
multiple knapsacks
bin packing
competitive analysis