Cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes

Authors:
Heiko Schröder;Ondrej Sýkora;Imrich Vrto
Affiliations:
School of Computer Science and Information Technology, RMIT University, GPO Box 2476v, Melbourne, Victoria 3001, Australia;Department of Computer Science, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK;Department of Informatics, Institute for Mathematics, Slovak Academy of Sciences, Dúbravská 9, Bratislava 841 04, Slovak Republic
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

The cutwidth problem is to find a linear layout of a network so that the maximal number of cuts of a line separating consecutive vertices is minimized (see e.g. [7]). A related and more natural problem is the cyclic cutwidth when a circular layout is considered. The main question is to compare both measures cw and ccw for specific networks, whether adding an edge to a path and forming a cycle reduces the cutwidth essentially. We prove exact values for the cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes Pm × Pn and Pm × Cn, respectively. Especially, if m ≥ n + 3, then ccw (Pm × Pn) = cw(Pm × Pn) = n + 1 and if n is even then ccw(Pn × Pn) = n - 1 while cw(Pm × Pn) = n + 1 and if m ≥ 2, n ≥ 3, then ccw(Pm × Cn) = min{m + 1, n + 2}.