Directed Symmetric Multicut is W[1]hard
Abstract
Given a directed graph $G$ and a set of vertex pairs $\{(s_1,t_1), \dots, (s_m, t_m)\}$, the Directed Symmetric Multicut problem asks to delete the minimum number of edges from $G$ to separate every pair $(s_i, t_i)$ into distinct strong components. Eiben, Rambaud and Wahlström [IPEC 2022] initiated the study of this problem parameterized by the solution size. They gave a fixedparameter tractable 2approximation algorithm, and left the exact parameterized complexity status as an open question. We answer their question in negative, showing that Directed Symmetric Multicut is W[1]hard.
 Publication:

arXiv eprints
 Pub Date:
 October 2023
 DOI:
 10.48550/arXiv.2310.05839
 arXiv:
 arXiv:2310.05839
 Bibcode:
 2023arXiv231005839O
 Keywords:

 Computer Science  Data Structures and Algorithms