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Vertex Bisection is hard, too (2009)

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by Ulrik Brandes , Daniel Fleischer
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BibTeX

@MISC{Brandes09vertexbisection,
    author = {Ulrik Brandes and Daniel Fleischer},
    title = {Vertex Bisection is hard, too},
    year = {2009}
}

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Abstract

We settle an open problem mentioned in Diaz, Petit, and Serna: A survey of graph layout problems (ACM Computing Surveys 34:313–356, 2002). Of eight objectives considered in that survey, only the complexity status of minimum vertex bisection is listed as unknown. We show that both minimum and maximum vertex bisection are N P-hard, but polynomially solvable on special graph classes such as hypercubes and trees.

Citations

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64 A polylogarithmic approximation of the minimum bisection - Feige, Krauthgamer - 2002
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5 On the bisection width and expansion of butterfly networks - Bornstein, Litman, et al.
5 The minimum bisection widths of the cube-connected cycles graph and cube graph - Manabe, Hagihara, et al. - 1984
4 The Relationship Between Gossiping in Vertex-Disjoint Paths Mode and Bisection Width - Klasing
4 Bisecting de Bruijn and Kautz graphs - Rolim, Tvrdik, et al. - 1998
3 On Partitioning a Graph: A Theoretical and Empirical Study - MacGregor - 1978
3 Upper and lower bounds for the optimal tree partitions - Palios - 1994
2 On the bisection width of partial k-trees - Soumyanath, Deogun - 1990
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