2024/10/23 by Fedor V. Fomin, Petr A. Golovach, Fomin, Fedor V. +7 · 3 citations
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.2410.17641
openalex publication_date 2024/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that Hedge Cut can be solved in quasipolynomial-time, raising the hope for a polynomial time algorithm. Jaffke, Lima, Masarík, Pilipczuk, and Souza [SODA 2023] complemented this result by showing that assuming the Exponential Time Hypothesis (ETH), no polynomial-time algorithm exists. In this paper, we show that Hedge Cut is fixed-parameter tractable parameterized by the solution size ℓ by providing an algorithm with running time \binomO(log n) + ℓℓ ⋅ mO(1), which can be upper bounded by cℓ ⋅ (n+m)O(1) for any constant c>1. This running time captures at the same time the fact that the problem is quasipolynomial-time solvable, and that it is fixed-parameter tractable parameterized by ℓ. We further generalize this algorithm to an algorithm with running time \binomO(k log n) + ℓℓ ⋅ nO(k) ⋅ mO(1) for Hedge k-Cut.