Hardness of approximation for strip packing

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Hardness of approximation for strip packing. / Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin; Pilipczuk, Michał.

I: ACM Transactions on Computation Theory, Bind 9, Nr. 3, 14, 09.2017.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Adamaszek, AM, Kociumaka, T, Pilipczuk, M & Pilipczuk, M 2017, 'Hardness of approximation for strip packing', ACM Transactions on Computation Theory, bind 9, nr. 3, 14. https://doi.org/10.1145/3092026

APA

Adamaszek, A. M., Kociumaka, T., Pilipczuk, M., & Pilipczuk, M. (2017). Hardness of approximation for strip packing. ACM Transactions on Computation Theory, 9(3), [14]. https://doi.org/10.1145/3092026

Vancouver

Adamaszek AM, Kociumaka T, Pilipczuk M, Pilipczuk M. Hardness of approximation for strip packing. ACM Transactions on Computation Theory. 2017 sep;9(3). 14. https://doi.org/10.1145/3092026

Author

Adamaszek, Anna Maria ; Kociumaka, Tomasz ; Pilipczuk, Marcin ; Pilipczuk, Michał. / Hardness of approximation for strip packing. I: ACM Transactions on Computation Theory. 2017 ; Bind 9, Nr. 3.

Bibtex

@article{388af3ad781a4265af3c2c112b969b03,
title = "Hardness of approximation for strip packing",
abstract = "Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively. When the dimensions of the objects are allowed to be exponential in the total input size, it is known that the problem cannot be approximated within a factor better than 3/2, unless P = NP. However, there was no corresponding lower bound for polynomially bounded input data. In fact, Nadiradze and Wiese [SODA 2016] have recently proposed a (1.4 + ϵ)-approximation algorithm for this variant, thus showing that strip packing with polynomially bounded data can be approximated better than when exponentially large values are allowed in the input. Their result has subsequently been improved to a (4/3 + ϵ)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two-dimensional knapsack. In this article, we answer this question in negative by proving that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data. In particular, this shows that the strip packing problem admits no quasi-polynomial time approximation scheme, unless NP ⊆ DTIME(2polylog(n)).",
keywords = "Approximation hardness, Packing problems, Strip packing",
author = "Adamaszek, {Anna Maria} and Tomasz Kociumaka and Marcin Pilipczuk and Michał Pilipczuk",
year = "2017",
month = "9",
doi = "10.1145/3092026",
language = "English",
volume = "9",
journal = "ACM Transactions on Computation Theory",
issn = "1942-3454",
publisher = "Association for Computing Machinery",
number = "3",

}

RIS

TY - JOUR

T1 - Hardness of approximation for strip packing

AU - Adamaszek, Anna Maria

AU - Kociumaka, Tomasz

AU - Pilipczuk, Marcin

AU - Pilipczuk, Michał

PY - 2017/9

Y1 - 2017/9

N2 - Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively. When the dimensions of the objects are allowed to be exponential in the total input size, it is known that the problem cannot be approximated within a factor better than 3/2, unless P = NP. However, there was no corresponding lower bound for polynomially bounded input data. In fact, Nadiradze and Wiese [SODA 2016] have recently proposed a (1.4 + ϵ)-approximation algorithm for this variant, thus showing that strip packing with polynomially bounded data can be approximated better than when exponentially large values are allowed in the input. Their result has subsequently been improved to a (4/3 + ϵ)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two-dimensional knapsack. In this article, we answer this question in negative by proving that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data. In particular, this shows that the strip packing problem admits no quasi-polynomial time approximation scheme, unless NP ⊆ DTIME(2polylog(n)).

AB - Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively. When the dimensions of the objects are allowed to be exponential in the total input size, it is known that the problem cannot be approximated within a factor better than 3/2, unless P = NP. However, there was no corresponding lower bound for polynomially bounded input data. In fact, Nadiradze and Wiese [SODA 2016] have recently proposed a (1.4 + ϵ)-approximation algorithm for this variant, thus showing that strip packing with polynomially bounded data can be approximated better than when exponentially large values are allowed in the input. Their result has subsequently been improved to a (4/3 + ϵ)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two-dimensional knapsack. In this article, we answer this question in negative by proving that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data. In particular, this shows that the strip packing problem admits no quasi-polynomial time approximation scheme, unless NP ⊆ DTIME(2polylog(n)).

KW - Approximation hardness

KW - Packing problems

KW - Strip packing

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U2 - 10.1145/3092026

DO - 10.1145/3092026

M3 - Journal article

VL - 9

JO - ACM Transactions on Computation Theory

JF - ACM Transactions on Computation Theory

SN - 1942-3454

IS - 3

M1 - 14

ER -

ID: 184140062