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Solving Directed Multiway Cut Faster Than 2ⁿ

Author Mingyu Xiao

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Author Details

Mingyu Xiao
  • School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

Funding

Mingyu Xiao acknowledges the National Science Foundation of China under Grant No. 62372095.

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Mingyu Xiao. Solving Directed Multiway Cut Faster Than 2ⁿ. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 104:1-104:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.104

Abstract

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|}).

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Exact Algorithms
  • Parameterized Algorithms
  • Directed Multiway Cut
  • Directed Multicut
  • Directed Graphs

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