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• W2951584599 abstract "In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| leq 1$ and there are at most $k$ edges with one endpoint in $A$ and the other in $B$. In this paper we give an algorithm for Minimum Bisection with running time $O(2^{O(k^{3})}n^3 log^3 n)$. This is the first fixed parameter tractable algorithm for Minimum Bisection. At the core of our algorithm lies a new decomposition theorem that states that every graph $G$ can be decomposed by small separators into parts where each part is highly connected in the following sense: any cut of bounded size can separate only a limited number of vertices from each part of the decomposition. Our techniques generalize to the weighted setting, where we seek for a bisection of minimum weight among solutions that contain at most $k$ edges." @default.
• W2951584599 created "2019-06-27" @default.
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• W2951584599 date "2013-11-11" @default.
• W2951584599 modified "2023-09-27" @default.
• W2951584599 title "Minimum Bisection is fixed parameter tractable" @default.
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• W2951584599 hasPublicationYear "2013" @default.
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