Optimal-size problem kernels for d-Hitting Set in linear time and space

René van Bevern; Pavel V. Smirnov

doi:10.1016/j.ipl.2020.105998

Optimal-size problem kernels for d-Hitting Set in linear time and space

René van Bevern, Pavel V. Smirnov

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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Аннотация

The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(k^d) for d-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for d-Hitting Set to each other and to a classical data reduction algorithm due to Weihe.

Язык оригинала	английский
Номер статьи	105998
Число страниц	9
Журнал	Information Processing Letters
Том	163
DOI	https://doi.org/10.1016/j.ipl.2020.105998
Состояние	Опубликовано - 1 ноя 2020

Предметные области OECD FOS+WOS

1.02 КОМПЬЮТЕРНЫЕ И ИНФОРМАЦИОННЫЕ НАУКИ

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title = "Optimal-size problem kernels for d-Hitting Set in linear time and space",

abstract = "The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(kd) for d-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for d-Hitting Set to each other and to a classical data reduction algorithm due to Weihe.",

keywords = "Combinatorial problems, Data reduction, Kernelization, NP-hard problem, Parameterized complexity",

author = "{van Bevern}, Ren{\'e} and Smirnov, {Pavel V.}",

year = "2020",

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language = "English",

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AU - van Bevern, René

AU - Smirnov, Pavel V.

PY - 2020/11/1

Y1 - 2020/11/1

N2 - The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(kd) for d-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for d-Hitting Set to each other and to a classical data reduction algorithm due to Weihe.

AB - The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(kd) for d-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for d-Hitting Set to each other and to a classical data reduction algorithm due to Weihe.

KW - Combinatorial problems

KW - Data reduction

KW - Kernelization

KW - NP-hard problem

KW - Parameterized complexity

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JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

M1 - 105998

ER -

Optimal-size problem kernels for d-Hitting Set in linear time and space

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