Eun Jung Kim, Tomáš Masařík, Marcin Pilipczuk, Roohani Sharma, Magnus Wahlström
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引用次数: 0
Abstract
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.
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.
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