Characteristic inequalities for binary trees
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by Roberto De Prisco
http://www.toc.lcs.mit.edu/~robdep/PS/kraft-DP95-ipl.ps.gz
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Abstract:
In a binary tree T of N leaves, the left (right) level l i (r i) of leaf i is the number of left (right) edges in path from the root to that leaf. The level n i of leaf i is n i = l i +r i. Kraft-McMillan's characteristic inequality gives a necessary and sufficient condition for a multiset of integers fn 1; n 2;:::; nN g to be the length ensemble of a binary tree T. Similarly, Yeung's characteristic inequality gives a necessary and sufficient condition for a vector of integers (n 1; n 2;:::; nN) to be the length vector of a binary tree T. In this paper, we study characteristic inequalities for the path ensemble f(l 1; r 1); (l 2; r 2);
Citations
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| 37 | The complexity of maintaining an array and computing its partial sums – Fredman - 1982 |
| 29 | Variable-length binary encodings – Gilbert, Moore - 1959 |
| 18 | Optimal biweighted binary trees and the complexity of maintaining partial sums – Hampapuram, Fredman - 1998 |
| 11 | Alphabetic codes revisited – Yeung - 1991 |
