Why it matters

Y-fast tries reduce vEB space to O(n). Rare in practice.

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The architecture

x-fast trie + bucket per leaf.

Balanced BST inside bucket.

O(log log U) ops.

Y-fast triex-fast + bucketshierarchicalBalanced BSTper bucketO(log log U)linear spaceWillard 1983; theoretically important; rarely used in practice
Y-fast trie.
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How it works end to end

Willard 1983.

O(log log U).

O(n) space.