In the Directed Multiway Cut problem, we are given a directed graph G = (V,E) and a subset T ⊆ V, called the terminal set. The aim is to find a minimum sized set S ⊆ V⧵ T, such that after deleting S, no directed path exists from one terminal to another terminal in the remaining graph. It has been an open question whether Directed Multiway Cut can be solved faster than the trivial running-time bound O^*(2^{|V|}). In this paper, we provide a positive answer to this question, presenting an algorithm with a running-time bound O(1.9967^{|V|}).
@InProceedings{xiao:LIPIcs.ESA.2024.104, author = {Xiao, Mingyu}, title = {{Solving Directed Multiway Cut Faster Than 2ⁿ}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {104:1--104:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.104}, URN = {urn:nbn:de:0030-drops-211758}, doi = {10.4230/LIPIcs.ESA.2024.104}, annote = {Keywords: Exact Algorithms, Parameterized Algorithms, Directed Multiway Cut, Directed Multicut, Directed Graphs} }
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