Cutwidth I: A linear time fixed parameter algorithm,☆☆

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Abstract

The cutwidth of a graph G is the smallest integer k such that the vertices of G can be arranged in a linear layout [v1,,vn] in such a way that, for every i=1,,n1, there are at most k edges with one endpoint in {v1,,vi} and the other in {vi+1,,vn}. In this paper we provide, for any constant k, a linear time algorithm that for any input graph G, answers whether G has cutwidth at most k and, in the case of a positive answer, outputs the corresponding linear layout.

References (22)

  • H.L. Bodlaender et al.

    Starting with nondeterminism: the systematic derivation of linear-time graph layout algorithms

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    The work of all the authors was supported by the EU project ALCOM-FT (IST-99-14186). The research of the first author was supported by the Spanish CICYT project TIC2000-1970-CE and the Ministry of Education and Culture of Spain (Resolución 31/7/00 – BOE 16/8/00).

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    This paper is the full version of part of the paper titled “Constructive linear time algorithms for small cutwidth and carving-width” which appeared in: Proceedings of 11th International Conference ISAAC 2000, Lectures Notes in Comput. Sci., vol. 1969, Springer-Verlag, 2000, pp. 192–203.

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