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- W4313429567 abstract "In the problem (Unweighted) Max-Cut we are given a graph $$G = (V,E)$$ and asked for a set $$S subseteq V$$ such that the number of edges from S to $$V setminus S$$ is maximal. In this paper we consider an even harder problem: (Weighted) Max-Bisection. Here we are given an undirected graph $$G = (V,E)$$ and a weight function $$w :E rightarrow mathbb {Q}_{>0}$$ and the task is to find a set $$S subseteq V$$ such that (i) the sum of the weights of edges from S is maximal; and (ii) S contains $$lceil * rceil {frac{n}{2}}$$ vertices (where $$n = | V |$$ ). We design a framework that allows to solve this problem in time $$mathcal {O}(2^t n^2)$$ if a tree decomposition of width t is given as part of the input. This improves the previously best running time for Max-Bisection of Hanaka, Kobayashi, and Sone [9] by a factor $$t^2$$ . Under common hardness assumptions, neither the dependence on t in the exponent nor the dependence on n can be reduced [7, 9, 16]. Our framework can be applied to other cut problems like Min-Edge-Expansion, Sparsest-Cut, Densest-Cut, $$beta $$ -Balanced-Min-Cut, and Min-Bisection. It also works in the setting with arbitrary weights and directed edges." @default.
- W4313429567 created "2023-01-06" @default.
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- W4313429567 date "2023-01-01" @default.
- W4313429567 modified "2023-10-14" @default.
- W4313429567 title "Solving Cut-Problems in Quadratic Time for Graphs with Bounded Treewidth" @default.
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- W4313429567 doi "https://doi.org/10.1007/978-3-031-23101-8_3" @default.
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