Cutwidth of the

We prove that the cutwidth of the r-dimensional mesh of d-ary trees is of order $\Theta(d^{(r-1)n+1})$, which improves and generalizes previous results

Cutwidth of the r-dimensional Mesh of d-ary Trees

We prove that the cutwidth of the r-dimensional mesh of d-ary trees is of order \Theta(d (r\Gamma1)n+1 ), which improves and generalizes the previous result of Barth [2]. Resum'e Nous provons que la largeur de coupe de la grille r-dimensionall d'arbres d-naires est d'ordre \Theta(d (r\Gamma1)n+1 ), que ameliore et generalise le resultat de Barth [2]. 2 1 Introduction The cutwidth is a fundamental parameter of interconnection networks which plays an important role in the VLSI design [7]. Informally, the cutwidth problem is to find a linear layout of vertices of a graph and a drawing of its edges as semiarcs above the line so that the maximum number of cuts of a vertical line separating consecutive vertices with edges is minimized. The corresponding decision problem is NP -complete in general but is solvable in polynomial time for trees [10]. Very little is known on the exact or even approximate values of the cutwidth of specific graphs, see e.g. [6, 8, 9]. We study the cutwidth..