Overview
Fibonacci Heap is a data structure that maintains an invariant that supports efficient queries, updates, summaries, or indexing. It trades implementation complexity for faster or more compact operations on repeated workloads.
CoreSource checked
Fibonacci Heap
Fibonacci Heap organizes data around a query, update, ordering, or approximation invariant.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Data Structures
- Difficulty
- Intermediate
- Family
- Data Structure
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
invariantquery operationupdate operationstorage layout
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(log n)
Worst
O(n)
Space
O(n)
When to Use
- Use Fibonacci Heap when repeated operations benefit from its invariant or summary structure.
- Use it when operation mix is stable enough to justify maintaining the structure.
When Not to Use
- Avoid when the workload is too small to justify the added invariant maintenance.
- Avoid when updates violate assumptions behind the query guarantees.
What It Does
- Organizes data for efficient access
- Maintains structural invariants
- Supports queries, inserts, deletes, or summaries
Use Cases
- Indexing data
- Caching
- Fast query processing
Inputs
- Items, keys, or graph records
- Queries or updates
Outputs
- Stored structure
- Query result
- Updated structure
Pseudocode
- 1.Initialize the structure and invariants
- 2.Apply insert, query, update, or delete operations
- 3.Rebalance, hash, summarize, or split nodes as needed
- 4.Return the query result or updated structure
Canonical Example
- Input
- operations = insert A, insert B, query A
- Output
- updated structure and query result
- Explanation
- Fibonacci Heap maintains its invariant while answering the requested operation.
Implementation Notes
- Write invariant checks for debug builds.
- Benchmark the expected query/update mix instead of isolated operations only.
Common Pitfalls
- Breaking the invariant during an update can make later queries silently wrong.
- Ignoring adversarial or skewed input can erase expected performance.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow the structure changing as items are inserted, queried, or removed.
Step 1 of 4: Initialize the structure and invariants
data-structureNotes
Fibonacci Heap operates in O(log n) time and O(n) space within the Data Structure family. Often compared with Heap and Priority Queue.
Sources (1)
What each reference supports for this entry.
Fibonacci Heaps
PaperOriginal reference for Fibonacci heap amortized operations and priority-queue improvements.
Open sourceExplore Next
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Variant ofHeap
Data Structures · Foundation
Fibonacci heaps are heap variants that support meldable priority queues with amortized decrease-key efficiency.
Compare with thisRelationships
View full relationship pageVariant ofHeap
Fibonacci heaps are heap variants that support meldable priority queues with amortized decrease-key efficiency.
Alternative toBinomial Heap
Fibonacci heaps improve on binomial-heap amortized costs by allowing lazy consolidation.
Related Algorithms
Tags
Data Structure