非循环匹配的参数化结果及其对相关问题的影响

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2024-10-21 DOI:10.1016/j.jcss.2024.103599

Juhi Chaudhary , Meirav Zehavi

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引用次数: 0

摘要

如果 M 的边的端点所诱导的 G 子图是一个森林，那么图 G 中的匹配 M 就是非循环匹配。给定一个图 G 和 ℓ∈N，非循环匹配问 G 是否有大小至少为 ℓ 的非循环匹配。在本文中，我们证明了假设 W[1]⊈FPT 时，不存在任何 FPT 近似算法，可以在以ℓ 为参数时，以常数因子内逼近 Acyclic Matching。我们的还原也证明了诱导匹配和唯一限制匹配的 FPT 近似性。我们还考虑了 Acyclic Matching 的三个低于保证的参数，即 n2-ℓ、MM(G)-ℓ 和 IS(G)-ℓ，其中 n=V(G), MM(G) 是匹配数，IS(G) 是 G 的独立数。此外，我们还证明，除非 NP⊆coNP/poly，否则无循环匹配并不表现出关于顶点覆盖数（或顶点到小块的删除距离）加上匹配大小的多项式内核。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Parameterized results on acyclic matchings with implications for related problems

A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and

ℓ \in N

, Acyclic Matching asks whether G has an acyclic matching of size at least ℓ. In this paper, we prove that assuming

W [1] ⊈ FPT

, there does not exist any

FPT

-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by ℓ. Our reduction also asserts

FPT

-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz.

\frac{n}{2} - ℓ

MM (G) - ℓ

, and

IS (G) - ℓ

, where

n = V (G)

MM (G)

is the matching number, and

IS (G)

is the independence number of G. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless

NP \subseteq coNP / poly

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.