Summary
It is shown that ¯n (N), the average number of nodes in an N-key random 2–3 tree, satisfies the inequality 0.70 N < ¯n(N) <0.79 N for large N. A similar analysis is done for general B-trees. It is shown that storage utilization is essentially ln 2≈69% for B-tree of high orders.
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This work was done while the author was at University of Illinois, partially supported by NSF Grant GJ 41538. The preparation of this paper has also been partially supported by NSF Grants MCS 72-06336 A04 and MCS 72-03752 A03
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Yao, A.CC. On random 2–3 trees. Acta Informatica 9, 159–170 (1978). https://doi.org/10.1007/BF00289075
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DOI: https://doi.org/10.1007/BF00289075