The packing problem is to pack given items into given containers as efficiently as possible under various constraints. It is fundamental and significant with variations and applications. The Set-Bin-Packing (SBP) is a class of packing problems: Pack given items into as few bins which have the same capacity where every item is a set and a bin can contain items as long as the number of distinct elements in the union of the items equals to or less than the capacity. One of applications is in FPGA technology mapping, which is our initial motivation. In this paper, the computational complexity of SBP is studied with respect to three parameters α, γ, and δ which are the capacity, the upper bound of the number of elements in an item, and the upper bound of the number of items having an element, respectively. In contrast that the well known Integer-Bin-Packing (IBP) is NP-hard but is proved that even a simplest heuristics First-Fit-Decreasing (FFD) outputs exact solutions as long as α
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Tomonori IZUMI, Toshihiko YOKOMARU, Atsushi TAKAHASHI, Yoji KAJITANI, "Computational Complexity Analysis of Set-Bin-Packing Problem" in IEICE TRANSACTIONS on Fundamentals,
vol. E81-A, no. 5, pp. 842-849, May 1998, doi: .
Abstract: The packing problem is to pack given items into given containers as efficiently as possible under various constraints. It is fundamental and significant with variations and applications. The Set-Bin-Packing (SBP) is a class of packing problems: Pack given items into as few bins which have the same capacity where every item is a set and a bin can contain items as long as the number of distinct elements in the union of the items equals to or less than the capacity. One of applications is in FPGA technology mapping, which is our initial motivation. In this paper, the computational complexity of SBP is studied with respect to three parameters α, γ, and δ which are the capacity, the upper bound of the number of elements in an item, and the upper bound of the number of items having an element, respectively. In contrast that the well known Integer-Bin-Packing (IBP) is NP-hard but is proved that even a simplest heuristics First-Fit-Decreasing (FFD) outputs exact solutions as long as α
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_5_842/_p
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@ARTICLE{e81-a_5_842,
author={Tomonori IZUMI, Toshihiko YOKOMARU, Atsushi TAKAHASHI, Yoji KAJITANI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Computational Complexity Analysis of Set-Bin-Packing Problem},
year={1998},
volume={E81-A},
number={5},
pages={842-849},
abstract={The packing problem is to pack given items into given containers as efficiently as possible under various constraints. It is fundamental and significant with variations and applications. The Set-Bin-Packing (SBP) is a class of packing problems: Pack given items into as few bins which have the same capacity where every item is a set and a bin can contain items as long as the number of distinct elements in the union of the items equals to or less than the capacity. One of applications is in FPGA technology mapping, which is our initial motivation. In this paper, the computational complexity of SBP is studied with respect to three parameters α, γ, and δ which are the capacity, the upper bound of the number of elements in an item, and the upper bound of the number of items having an element, respectively. In contrast that the well known Integer-Bin-Packing (IBP) is NP-hard but is proved that even a simplest heuristics First-Fit-Decreasing (FFD) outputs exact solutions as long as α
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Computational Complexity Analysis of Set-Bin-Packing Problem
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 842
EP - 849
AU - Tomonori IZUMI
AU - Toshihiko YOKOMARU
AU - Atsushi TAKAHASHI
AU - Yoji KAJITANI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1998
AB - The packing problem is to pack given items into given containers as efficiently as possible under various constraints. It is fundamental and significant with variations and applications. The Set-Bin-Packing (SBP) is a class of packing problems: Pack given items into as few bins which have the same capacity where every item is a set and a bin can contain items as long as the number of distinct elements in the union of the items equals to or less than the capacity. One of applications is in FPGA technology mapping, which is our initial motivation. In this paper, the computational complexity of SBP is studied with respect to three parameters α, γ, and δ which are the capacity, the upper bound of the number of elements in an item, and the upper bound of the number of items having an element, respectively. In contrast that the well known Integer-Bin-Packing (IBP) is NP-hard but is proved that even a simplest heuristics First-Fit-Decreasing (FFD) outputs exact solutions as long as α
ER -