Balance in AVL trees and space cost of brother trees

Helen Cameron, Derick Wood
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Abstraci Cameron, H. and D. Wood, Balance in AVL trees and space cost of brother trees, Theoretical Computer Science 127 (1994) 199-228. We characterize AVL trees that have, for their heights and weights, the maximum numbers of nodes whose subtrees differ in height by one (imbalanced nodes). We obtain the result from a characterization of brother trees with the maximum space costs for their heights and weights. The proof is based on a novel tree transformation that is of interest in its own right.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/0304-3975(94)90040-x</a> <a target="_blank" rel="external noopener" href="">fatcat:f6vczb76cvesxihma3els6fy7q</a> </span>
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