论加权图分离问题和流量增强

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-08 DOI:10.1137/22m153118x

Eun Jung Kim, Tomáš Masařík, Marcin Pilipczuk, Roohani Sharma, Magnus Wahlström

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 170-189 页，2024 年 3 月。摘要最近引入的流增强技术[Kim 等人，STOC 2022]的首批应用之一是加权版定向反馈顶点集的固定参数算法，这是参数化复杂度的一个标志性问题。在本文中，我们探讨了流量增强对其他以切集大小为参数的加权图分离问题的适用性。我们展示了以下内容：在加权无向图中，Multicut 在边和顶点删除版本中都是固定参数可处理（FPT）的。群反馈顶点集的加权版本是 FPT，甚至可以用甲骨文访问群操作。有向子集反馈顶点集合的加权版本是 FPT。我们的研究揭示了有向对称多重图是下一个重要的图分离问题，它的参数化复杂度仍是未知的，即使在无权设置中也是如此。

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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On Weighted Graph Separation Problems and Flow Augmentation

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 170-189, March 2024.
Abstract. One of the first applications of the recently introduced technique of flow augmentation [Kim et al., STOC 2022] is a fixed-parameter algorithm for the weighted version of Directed Feedback Vertex Set, a landmark problem in parameterized complexity. In this article, we explore the applicability of flow augmentation to other weighted graph separation problems parameterized by the size of the cutset. We show the following: In weighted undirected graphs, Multicut is fixed-parameter tractable (FPT) in both the edge- and the vertex-deletion version. The weighted version of Group Feedback Vertex Set is FPT, even with oracle access to group operations. The weighted version of Directed Subset Feedback Vertex Set is FPT. Our study reveals Directed Symmetric Multicut as the next important graph separation problem whose parameterized complexity remains unknown, even in the unweighted setting.

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.