Parameterized complexity of Strip Packing and Minimum Volume Packing

Pradeesha Ashok; Sudeshna Kolay; S. M. Meesum; Saket Saurabh

doi:10.1016/j.tcs.2016.11.034

Parameterized complexity of Strip Packing and Minimum Volume Packing

Pradeesha Ashok, Sudeshna Kolay, S. M. Meesum, Saket Saurabh

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We study the parameterized complexity of MINIMUM VOLUME PACKING and STRIP PACKING. In the two dimensional version the input consists of a set of rectangles S with integer side lengths. In the MINIMUM VOLUME PACKING problem, given a set of rectangles S and a number k, the goal is to decide if the rectangles can be packed in a bounding box of volume at most k. In the STRIP PACKING problem we are given a set of rectangles S, numbers W and k; the objective is to find if all the rectangles can be packed in a box of dimensions W×k. We prove that the 2-dimensional VOLUME PACKING is in FPT by giving an algorithm that runs in (2⋅2)^k⋅k^O(1) time. We also show that STRIP PACKING is W[1]-hard even in two dimensions and give an FPT algorithm for a special case of STRIP PACKING. Some of our results hold for the problems defined in higher dimensions as well.

Original language	English
Pages (from-to)	56-64
Number of pages	9
Journal	Theoretical Computer Science
Volume	661
DOIs	https://doi.org/10.1016/j.tcs.2016.11.034
State	Published - 24 Jan 2017
Externally published	Yes

Keywords

Greedy packing
Strip Packing
Volume minimization

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2016.11.034

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title = "Parameterized complexity of Strip Packing and Minimum Volume Packing",

abstract = "We study the parameterized complexity of MINIMUM VOLUME PACKING and STRIP PACKING. In the two dimensional version the input consists of a set of rectangles S with integer side lengths. In the MINIMUM VOLUME PACKING problem, given a set of rectangles S and a number k, the goal is to decide if the rectangles can be packed in a bounding box of volume at most k. In the STRIP PACKING problem we are given a set of rectangles S, numbers W and k; the objective is to find if all the rectangles can be packed in a box of dimensions W×k. We prove that the 2-dimensional VOLUME PACKING is in FPT by giving an algorithm that runs in (2⋅2)k⋅kO(1) time. We also show that STRIP PACKING is W[1]-hard even in two dimensions and give an FPT algorithm for a special case of STRIP PACKING. Some of our results hold for the problems defined in higher dimensions as well.",

keywords = "Greedy packing, Strip Packing, Volume minimization",

author = "Pradeesha Ashok and Sudeshna Kolay and Meesum, {S. M.} and Saket Saurabh",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

month = jan,

day = "24",

doi = "10.1016/j.tcs.2016.11.034",

language = "English",

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T1 - Parameterized complexity of Strip Packing and Minimum Volume Packing

AU - Ashok, Pradeesha

AU - Kolay, Sudeshna

AU - Meesum, S. M.

AU - Saurabh, Saket

PY - 2017/1/24

Y1 - 2017/1/24

N2 - We study the parameterized complexity of MINIMUM VOLUME PACKING and STRIP PACKING. In the two dimensional version the input consists of a set of rectangles S with integer side lengths. In the MINIMUM VOLUME PACKING problem, given a set of rectangles S and a number k, the goal is to decide if the rectangles can be packed in a bounding box of volume at most k. In the STRIP PACKING problem we are given a set of rectangles S, numbers W and k; the objective is to find if all the rectangles can be packed in a box of dimensions W×k. We prove that the 2-dimensional VOLUME PACKING is in FPT by giving an algorithm that runs in (2⋅2)k⋅kO(1) time. We also show that STRIP PACKING is W[1]-hard even in two dimensions and give an FPT algorithm for a special case of STRIP PACKING. Some of our results hold for the problems defined in higher dimensions as well.

AB - We study the parameterized complexity of MINIMUM VOLUME PACKING and STRIP PACKING. In the two dimensional version the input consists of a set of rectangles S with integer side lengths. In the MINIMUM VOLUME PACKING problem, given a set of rectangles S and a number k, the goal is to decide if the rectangles can be packed in a bounding box of volume at most k. In the STRIP PACKING problem we are given a set of rectangles S, numbers W and k; the objective is to find if all the rectangles can be packed in a box of dimensions W×k. We prove that the 2-dimensional VOLUME PACKING is in FPT by giving an algorithm that runs in (2⋅2)k⋅kO(1) time. We also show that STRIP PACKING is W[1]-hard even in two dimensions and give an FPT algorithm for a special case of STRIP PACKING. Some of our results hold for the problems defined in higher dimensions as well.

KW - Greedy packing

KW - Strip Packing

KW - Volume minimization

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DO - 10.1016/j.tcs.2016.11.034

M3 - Article

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SN - 0304-3975

VL - 661

SP - 56

EP - 64

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Parameterized complexity of Strip Packing and Minimum Volume Packing

Abstract

Keywords

ASJC Scopus subject areas

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