遗忘可以让你更快:一个O*(8.097k)时间的加权3集k-包装算法

IF 0.8 Q3 COMPUTER SCIENCE, THEORY & METHODS
M. Zehavi
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引用次数: 0

摘要

本文研究了经典的加权3集k- packing问题:给定一个域U,一个U的大小为3的子集族\(\mathcal {S} \),一个权函数\(w : {\mathcal {S}} \rightarrow \mathbb {R} \), \(W \in \mathbb {R} \)和一个参数\(k \in \mathbb {N} \),目的是确定是否存在k个不相交集的子族\({\mathcal {S}}^{\prime } \subseteq {\mathcal {S}} \),并且总权值至少为w。我们给出了一个确定性参数化算法,该算法运行时间为O*(8.097k),其中O*隐藏了输入大小中的因子多项式。这大大改进了之前加权3集k-Packing的最佳确定性算法,该算法运行时间为O*(12.155k) [SIDMA 2015],也是该问题的非加权版本的最佳确定性算法。我们的算法是基于代表集方法的一种新的应用,这可能是独立的兴趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Forgetfulness Can Make You Faster: An O*(8.097k)-Time Algorithm for Weighted 3-Set k-Packing
In this paper, we study the classic Weighted 3-Set k-Packing problem: given a universe U, a family \(\mathcal {S} \) of subsets of size 3 of U, a weight function \(w : {\mathcal {S}} \rightarrow \mathbb {R} \) , \(W \in \mathbb {R} \) and a parameter \(k \in \mathbb {N} \) , the objective is to decide if there is a subfamily \({\mathcal {S}}^{\prime } \subseteq {\mathcal {S}} \) of k disjoint sets and total weight at least W. We present a deterministic parameterized algorithm for this problem that runs in time O*(8.097k), where O* hides factors polynomial in the input size. This substantially improves upon the previously best deterministic algorithm for Weighted 3-Set k-Packing, which runs in time O*(12.155k) [SIDMA 2015], and was also the best deterministic algorithm for the unweighted version of this problem. Our algorithm is based on a novel application of the method of representative sets that might be of independent interest.
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来源期刊
ACM Transactions on Computation Theory
ACM Transactions on Computation Theory COMPUTER SCIENCE, THEORY & METHODS-
CiteScore
2.30
自引率
0.00%
发文量
10
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