On one problem of Koffman-Shor connected to strip packing problem
In 1993 Coffman and Shor proposed on-line strip packing algorithm with expected unpacked area (waste area) of order O(n^{2/3}) in a standard probabilistic model, where n is the number of rectangles. In the standard probabilistic model the width and height of each rectangle are independent random var...
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| Format: | Article |
| Language: | English |
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Ivannikov Institute for System Programming of the Russian Academy of Sciences
2018-10-01
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| Series: | Труды Института системного программирования РАН |
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| Online Access: | https://ispranproceedings.elpub.ru/jour/article/view/1022 |
| _version_ | 1828530775349264384 |
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| author | M. A. Trushnikov |
| author_facet | M. A. Trushnikov |
| author_sort | M. A. Trushnikov |
| collection | DOAJ |
| description | In 1993 Coffman and Shor proposed on-line strip packing algorithm with expected unpacked area (waste area) of order O(n^{2/3}) in a standard probabilistic model, where n is the number of rectangles. In the standard probabilistic model the width and height of each rectangle are independent random variables with uniform distribution in [0,1]. It is well-known that optimal packing has expected waste of order O(n^{1/2}) and there exists off-line polynomial algorithm that provides this bound.. During more than 10 years the question concerning the possibility to obtain similar upper bound in the class of on-line strip packing algorithms was open. It was also known that in the class of popular so-called shelf algorithms the bound O(n^{2/3}) cannot be improved. In this paper we propose new strip packing algorithm which differs from all known on-line strip packing algorithms. We analyze our strip packing algorithm experimentally and show that the upper bound of expected unpacked area is of order O(n^{1/2}) which is optimal up to constant factor. Our experimnets show that this constant factor is close to 1.5-1.6. Our experiments were done with up to 2000000000 random rectangles. The only restriction is the following: we must know the number n of rectangles in advance. In a popular terminology concerning on-line algorithms this means that our algorithm is closed-end on-line algorithm.The paper proposes a new online strip packing algorithm that provides a quality of packing significantly higher than well-known algorithm of Koffman-Shor. |
| first_indexed | 2024-12-11T22:27:58Z |
| format | Article |
| id | doaj.art-d42d07fa4b534b35b3b051fd8b81dab3 |
| institution | Directory Open Access Journal |
| issn | 2079-8156 2220-6426 |
| language | English |
| last_indexed | 2024-12-11T22:27:58Z |
| publishDate | 2018-10-01 |
| publisher | Ivannikov Institute for System Programming of the Russian Academy of Sciences |
| record_format | Article |
| series | Труды Института системного программирования РАН |
| spelling | doaj.art-d42d07fa4b534b35b3b051fd8b81dab32022-12-22T00:48:14ZengIvannikov Institute for System Programming of the Russian Academy of SciencesТруды Института системного программирования РАН2079-81562220-64262018-10-012201022On one problem of Koffman-Shor connected to strip packing problemM. A. Trushnikov0ИСП РАНIn 1993 Coffman and Shor proposed on-line strip packing algorithm with expected unpacked area (waste area) of order O(n^{2/3}) in a standard probabilistic model, where n is the number of rectangles. In the standard probabilistic model the width and height of each rectangle are independent random variables with uniform distribution in [0,1]. It is well-known that optimal packing has expected waste of order O(n^{1/2}) and there exists off-line polynomial algorithm that provides this bound.. During more than 10 years the question concerning the possibility to obtain similar upper bound in the class of on-line strip packing algorithms was open. It was also known that in the class of popular so-called shelf algorithms the bound O(n^{2/3}) cannot be improved. In this paper we propose new strip packing algorithm which differs from all known on-line strip packing algorithms. We analyze our strip packing algorithm experimentally and show that the upper bound of expected unpacked area is of order O(n^{1/2}) which is optimal up to constant factor. Our experimnets show that this constant factor is close to 1.5-1.6. Our experiments were done with up to 2000000000 random rectangles. The only restriction is the following: we must know the number n of rectangles in advance. In a popular terminology concerning on-line algorithms this means that our algorithm is closed-end on-line algorithm.The paper proposes a new online strip packing algorithm that provides a quality of packing significantly higher than well-known algorithm of Koffman-Shor.https://ispranproceedings.elpub.ru/jour/article/view/1022онлайновый алгоритм упаковки прямоугольников в полосу, алгоритм коффмана-шора |
| spellingShingle | M. A. Trushnikov On one problem of Koffman-Shor connected to strip packing problem Труды Института системного программирования РАН онлайновый алгоритм упаковки прямоугольников в полосу, алгоритм коффмана-шора |
| title | On one problem of Koffman-Shor connected to strip packing problem |
| title_full | On one problem of Koffman-Shor connected to strip packing problem |
| title_fullStr | On one problem of Koffman-Shor connected to strip packing problem |
| title_full_unstemmed | On one problem of Koffman-Shor connected to strip packing problem |
| title_short | On one problem of Koffman-Shor connected to strip packing problem |
| title_sort | on one problem of koffman shor connected to strip packing problem |
| topic | онлайновый алгоритм упаковки прямоугольников в полосу, алгоритм коффмана-шора |
| url | https://ispranproceedings.elpub.ru/jour/article/view/1022 |
| work_keys_str_mv | AT matrushnikov ononeproblemofkoffmanshorconnectedtostrippackingproblem |