Cited By
View all- Mandal SMisra PRai ASaurabh S(2024)Parameterized Approximation Algorithms for Weighted Vertex CoverLATIN 2024: Theoretical Informatics10.1007/978-3-031-55601-2_12(177-192)Online publication date: 18-Mar-2024
Parameterized Complexity of Weighted Multicut in Trees
Authors: 
Esther Galby, Dániel Marx, Philipp Schepper, Roohani Sharma, Prafullkumar TaleAuthors Info & Claims
Esther Galby, Dániel Marx, Philipp Schepper, Roohani Sharma, Prafullkumar TaleAuthors Info & ClaimsPages 257 - 270
Abstract
The Edge Multicut problem is a classical cut problem where given an undirected graph G, a set of pairs of vertices, and a budget, the goal is to determine if there is a set S of at most edges such that for each, has no path from s to t. Edge Multicut has been relatively recently shown to be fixed-parameter tractable (FPT), parameterized by, by Marx and Razgon [SICOMP 2014], and independently by Bousquet et al. [SICOMP 2018]. In the weighted version of the problem, called Weighted Edge Multicut one is additionally given a weight function and a weight bound, and the goal is to determine if there is a solution of size at most and weight at most . Both the FPT algorithms for Edge Multicut by Marx et al. and Bousquet et al. fail to generalize to the weighted setting. In fact, the weighted problem is non-trivial even on trees and determining whether Weighted Edge Multicut on trees is FPT was explicitly posed as an open problem by Bousquet et al. [STACS 2009]. In this article, we answer this question positively by designing an algorithm which uses a very recent result by Kim et al. [STOC 2022] about directed flow augmentation as subroutine.
We also study a variant of this problem where there is no bound on the size of the solution, but the parameter is a structural property of the input, for example, the number of leaves of the tree. We strengthen our results by stating them for the more general vertex deletion version.
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Jun 2022
468 pages
© Springer Nature Switzerland AG 2022.
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Published: 22 June 2022
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View all- Mandal SMisra PRai ASaurabh S(2024)Parameterized Approximation Algorithms for Weighted Vertex CoverLATIN 2024: Theoretical Informatics10.1007/978-3-031-55601-2_12(177-192)Online publication date: 18-Mar-2024