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http://hdl.handle.net/11320/12391
Tytuł: | Algorithm NextFit for the Bin Packing Problem |
Autorzy: | Fujiwara, Hiroshi Adachi, Ryota Yamamoto, Hiroaki |
Słowa kluczowe: | bin packing problem online algorithm approximation algorithm combinatorial optimization |
Data wydania: | 2021 |
Data dodania: | 4-sty-2022 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 29, Issue 3, Pages 141-151 |
Abstrakt: | The bin packing problem is a fundamental and important optimization problem in theoretical computer science [4], [6]. An instance is a sequence of items, each being of positive size at most one. The task is to place all the items into bins so that the total size of items in each bin is at most one and the number of bins that contain at least one item is minimum. Approximation algorithms have been intensively studied. Algorithm NextFit would be the simplest one. The algorithm repeatedly does the following: If the first unprocessed item in the sequence can be placed, in terms of size, additionally to the bin into which the algorithm has placed an item the last time, place the item into that bin; otherwise place the item into an empty bin. Johnson [5] proved that the number of the resulting bins by algorithm NextFit is less than twice the number of the fewest bins that are needed to contain all items. In this article, we formalize in Mizar [1], [2] the bin packing problem as follows: An instance is a sequence of positive real numbers that are each at most one. The task is to find a function that maps the indices of the sequence to positive integers such that the sum of the subsequence for each of the inverse images is at most one and the size of the image is minimum. We then formalize algorithm NextFit, its feasibility, its approximation guarantee, and the tightness of the approximation guarantee. |
Afiliacja: | Hiroshi Fujiwara - Shinshu University, Nagano, Japan Ryota Adachi - Intage Technosphere Inc., Tokyo, Japan Hiroaki Yamamoto - Shinshu University, Nagano, Japan |
Opis: | This work was supported by JSPS KAKENHI Grant Numbers JP20K11689, JP20K11676, JP16K00033, JP17K00013, JP20K11808, and JP17K00183. |
URI: | http://hdl.handle.net/11320/12391 |
DOI: | 10.2478/forma-2021-0014 |
ISSN: | 1426–2630 |
e-ISSN: | 1898-9934 |
Typ Dokumentu: | Article |
Właściciel praw: | © 2021 University of Białymstoku CC-BY-SA License ver. 3.0 or later |
Występuje w kolekcji(ach): | Formalized Mathematics, 2021, Volume 29, Issue 3 |
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