Parameterized complexity of multicut in weighted trees

In the Multicut problem, given an undirected graph G, a set of pairs of vertices P, and a budget k, the goal is to determine if there is a set S of at most k edges such that for each (s,t)∈P, the graph G−S has no path from s to t. In this article we first study the parameterized complexity of a vari...

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Vydáno v:Theoretical computer science Ročník 978; s. 114174
Hlavní autoři: Galby, Esther, Marx, Dániel, Schepper, Philipp, Sharma, Roohani, Tale, Prafullkumar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 02.11.2023
Témata:
Directed flow augmentation
Multicut in weighted trees
Weighted digraph pair cut
Multicut in weighted trees
Weighted digraph pair cut
Directed flow augmentation
ISSN:0304-3975
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Shrnutí:In the Multicut problem, given an undirected graph G, a set of pairs of vertices P, and a budget k, the goal is to determine if there is a set S of at most k edges such that for each (s,t)∈P, the graph G−S has no path from s to t. In this article we first study the parameterized complexity of a variant of this problem, where the input graph is edge-weighted with arbitrary weights and the goal is to find a solution of minimum weight. Since weights are arbitrarily large, the weight of the solution is not a good choice for a parameter. The weighted problem is non-trivial even on trees and we study this problem on trees parameterized by structural parameters like the number of leaves and the request degree of every vertex. The studied parameters naturally interpolate the known polynomial time and NP-hardness results for this problem. We also give an FPT algorithm for another variant called Weighted Multicut, where given an edge-weighted tree, the goal is to find a solution of size at most k edges that minimizes the weight.
ISSN:0304-3975
DOI:10.1016/j.tcs.2023.114174