Work

Cutting Up Is Hard To Do

Year: 2003

Type: article

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].

Source: Electronic Notes in Theoretical Computer Science

DOI: 10.1016/s1571-0661(04)81014-4

Authors: Rodney G. Downey, Vladimir Estivill-Castro, Michael Fellows, Elena Prieto, Frances A. Rosamund

Institutions: Victoria University of Wellington, Griffith University, University of Newcastle Australia

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W1519147138

FWCI: 11.65

Cites: 33

Cited by: 123

Related to: 10