Cutting Up is Hard to Do: The Parameterised Complexity of k-Cut and Related Problems

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Abstract

The Graph k-Cut problem is that of finding a set of edges of minimum total weight, in an edge-weighted graph, such that their removal from the graph results in a graph having at least k connected components. An algorithm with a running time of O(nk2) for this problem has been known since 1988, due to Goldschmidt and Hochbaum. We show that the problem is hard for the parameterized complexity class W[1]. We also investigate the complexity of a related problem, CUTTING A FEW VERTICES FROM A GRAPH, that asks for the minimum cost of separating at least k vertices from an edge-weighted connected graph. We show that this problem also is hard for W[1].

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Downey, R. G., Estivill-Castro, V., Fellows, M., Prieto, E., & Rosamund, F. A. (2003). Cutting Up is Hard to Do: The Parameterised Complexity of k-Cut and Related Problems. In Electronic Notes in Theoretical Computer Science (Vol. 78, pp. 215–228). https://doi.org/10.1016/S1571-0661(04)81014-4

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