Abstract
The k-Min-Cut (k-Max-Cut) problem consists of partitioning the vertices of an edge weighted (undirected) graph into k sets so as to minimize (maximize) the sum of the weights of the edges joining vertices in different subsets. We concentrate on the k-Max-Cut and k-Min-Cut problems defined over complete graphs that satisfy the triangle inequality, as well as on d-dimensional graphs. For the one-dimensional version of our partitioning problems, we present efficient algorithms for their solution as well as lower bounds for the time required to find an optimal solution, and for the time required to verify that a solution is an optimal one. We also establish a bound for the objective function value of an optimal solution to the k-Min-Cut and k-Max-Cut problems whose graph satisfies the triangle inequality. The existence of this bound is important because it implies that any feasible solution is a near-optimal approximation to such versions of the k-Max-Cut and k-Min-Cut problems.
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© 1992 Springer-Verlag Berlin Heidelberg
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Gonzalez, T.F., Murayama, T. (1992). Algorithms for a class of Min-Cut and Max-Cut problem. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_62
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DOI: https://doi.org/10.1007/3-540-56279-6_62
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