An improved kernel for Max-Bisection above tight lower bound
Theoretical Computer Science(2020)
摘要
We study kernelizations for Max-Bisection above Tight Lower Bound, which is to decide if a given graph G=(V,E) admits a bisection with at least ⌈|E|/2⌉+k crossing edges. The best known kernel for this problem has 16k vertices. Based on the Gallai–Edmonds decomposition, we divide the vertices of G into several categories and study the roles of vertices in each category for obtaining a larger number of crossing edges. By making use of the properties of maximum matchings in G, graph G is partitioned into a set of blocks, and each block in G is closely related to the number of crossing edges of a bisection of G. By analyzing the number of crossing edges in blocks, an improved kernel of 8k vertices is presented.
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关键词
Max-Bisection,Gallai–Edmonds decomposition,Kernelization
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