- Search Trees with Relaxed Balance and Near-Optimal Height.
- Rolf Fagerberg, Rune E. Jensen, and Kim S. Larsen.
In 7th International Workshop on Algorithms and Data Structures (WADS), volume 2125 of Lecture Notes in Computer Science, pages 414-425. Springer, 2001.
We introduce a relaxed k
-tree, a search tree with relaxed balance
and a height bound, when in balance, of (1+epsilon)log_2 n + 1
for any epsilon > 0
The number of nodes involved in rebalancing is O(1/epsilon)
per update in the amortized sense,
and O(log n/epsilon)
in the worst case sense.
This is the first binary
search tree with relaxed balance having a height bound better than
c log_2 n
for a fixed constant c
. In all previous
proposals, the constant is at least 1/log_2 phi>1.44
is the golden ratio.
As a consequence, we can also define a standard (non-relaxed)
k-tree with amortized constant rebalancing, which is an
improvement over the current definition.
World Wide Web search engines are possible applications for this
line of work.
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