Bandwidths and profiles of trees

The bandwidths of labeled, rooted trees are studied. It is shown that the average bandwidth of trees of n vertices is >C1n and <C2n log n. The width of such a tree is the largest number of vertices at a constant distance from the root. The distribution of the width and its relationship with the bandwidth are studied. Results include generating functions for trees by width, and asymptotic estimates.

[1]  V. Chvátal,et al.  A remark on a problem of Harary , 1970 .

[2]  A. Rényi,et al.  On the height of trees , 1967, Journal of the Australian Mathematical Society.

[3]  James B. Saxe,et al.  Dynamic-Programming Algorithms for Recognizing Small-Bandwidth Graphs in Polynomial Time , 1980, SIAM J. Algebraic Discret. Methods.

[4]  Philippe Flajolet,et al.  The Average Height of Binary Trees and Other Simple Trees , 1982, J. Comput. Syst. Sci..

[5]  David S. Johnson,et al.  COMPLEXITY RESULTS FOR BANDWIDTH MINIMIZATION , 1978 .

[6]  J. Moon,et al.  On the Altitude of Nodes in Random Trees , 1978, Canadian Journal of Mathematics.

[7]  Jonathan S. Turner.  Probabilistic analysis of bandwidth minimization algorithms , 1983, STOC '83.