Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

被引：0

作者：

van Bevern, Rene ^{[1
]}

Kirilin, Artem M. ^{[2
]}

Skachkov, Daniel A. ^{[3
]}

Smirnov, Pavel V. ^{[4
]}

Tsidulko, Oxana Yu. ^{[5
]}

机构：

[1] Huawei Technol Co Ltd, Novosibirsk, Russia

[2] Siberian Fed Univ, Krasnoyarsk, Russia

[3] Moscow Inst Phys & Technol, Moscow, Russia

[4] Recraft, London, England

[5] Sobolev Inst Math, Novosibirsk, Russia

来源：

JOURNAL OF COMPUTER AND SYSTEM SCIENCES | 2024年 / 139卷

基金：

俄罗斯基础研究基金会;

关键词：

NP-hard problem; Data reduction; Problem kernelization; Parallel algorithm; Computational experiment; GPU; Parameterized complexity; ALGORITHMS; COMPLEXITY; GRAPHS;

D O I：

10.1016/j.jcss.2023.103479

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The NP-hard Multiple Hitting Set problem is the problem of finding a minimumcardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasibility of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Data) architectures.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：17