Overview
Y-Fast Trie is a integer dictionaries method for predecessor queries. It works by combining x-fast trie representatives with balanced buckets.
SpecializedSource checked
Y-Fast Trie
Y-Fast Trie addresses predecessor queries by combining x-fast trie representatives with balanced buckets.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Data Structures
- Difficulty
- Advanced
- Family
- Integer Dictionaries
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 3
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
predecessor queriesinteger dictionariesdata structures
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use Y-Fast Trie when solving predecessor queries and you want to benefit from combining x-fast trie representatives with balanced buckets.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over X-Fast Trie or Trie when the problem structure favors predecessor queries.
When Not to Use
- Avoid when the query pattern is too simple to justify the structure's overhead.
- Avoid when memory layout or rebuild cost dominates the expected speedup.
What It Does
- Computes predecessor queries within Integer Dictionaries workloads (O(n log n) time, O(n) space).
- Works by combining x-fast trie representatives with balanced buckets.
- Maintains key invariants across predecessor queries, integer dictionaries, data structures.
Use Cases
- Production and research workloads requiring predecessor queries via combining x-fast trie representatives with balanced buckets.
- Integer Dictionaries pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against X-Fast Trie and Trie when tuning predecessor queries.
Inputs
- Keys, values, items, or graph records
- Operations such as insert, delete, or query
Outputs
- Stored structure state
- Query result or updated collection
Pseudocode
- 1.Allocate the node layout, bit-vectors, or hierarchical buckets required by Y-Fast Trie.
- 2.Establish structural invariants over predecessor queries and integer dictionaries.
- 3.Execute queries or updates by combining x-fast trie representatives with balanced buckets.
- 4.Rebalance, split/merge, or refresh auxiliary pointers to preserve logarithmic/sub-logarithmic bounds.
- 5.Return the queried value, membership result, or updated structure handle.
Canonical Example
- Input
- Keys, values, items, or graph records configured for a representative predecessor queries test case
- Output
- Stored structure state satisfying Y-Fast Trie invariants
- Explanation
- Y-Fast Trie processes the input by combining x-fast trie representatives with balanced buckets, tracking predecessor queries and integer dictionaries to produce the verified predecessor queries result.
Implementation Notes
- Measure operations separately for insert, delete, query, and rebuild.
- Expose invariants in tests when balancing or compression is involved.
- Account for memory layout when performance matters.
Common Pitfalls
- Choosing the structure without matching it to the query/update pattern.
- Ignoring worst-case behavior behind favorable average-case examples.
- Forgetting memory overhead and rebuild costs.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow combining x-fast trie representatives with balanced buckets on a small predecessor queries example.
Step 1 of 5: Allocate the node layout, bit-vectors, or hierarchical buckets required by Y-Fast Trie.
data-structures-mechanismNotes
Y-Fast Trie operates in O(n log n) time and O(n) space within the Integer Dictionaries family. Often compared with X-Fast Trie and Trie.
Sources (1)
What each reference supports for this entry.
Handbook of Data Structures and Applications
BookData-structures reference for Y-fast tries, sampled representatives, and balanced-bucket predecessor search.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborX-Fast Trie
Y-Fast Trie and X-Fast Trie share a concrete integer dictionaries mechanism for predecessor queries.
Conceptual neighborTrie
Y-Fast Trie and Trie share a concrete integer dictionaries mechanism for predecessor queries.
Related Algorithms
Tags
Data Structure