Big-O notation
E679192
Big-O notation is a mathematical tool used in computer science to describe how the running time or space requirements of an algorithm grow relative to the size of its input.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Big-O notation canonical | 3 |
| Landau notation | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T7666918 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Big-O notation Context triple: [Complexity Theory, usesConcept, Big-O notation]
-
A.
Bounding Theory
Bounding Theory is a subtheory within Government and Binding Theory in generative linguistics that constrains how far syntactic elements can move in a sentence.
-
B.
Bounds
Bounds is the maiden surname of Lillian Disney, the wife of Walt Disney and a key figure in the early Disney family history.
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C.
Amdahl's law
Amdahl's law is a formula in computer architecture and parallel computing that predicts the maximum performance improvement achievable by parallelizing parts of a system, given that some portion must remain serial.
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D.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
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E.
Stirling's approximation
Stirling's approximation is a classical formula in mathematics that provides an efficient asymptotic estimate for factorials and the gamma function, especially for large arguments.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Big-O notation Target entity description: Big-O notation is a mathematical tool used in computer science to describe how the running time or space requirements of an algorithm grow relative to the size of its input.
-
A.
Bounding Theory
Bounding Theory is a subtheory within Government and Binding Theory in generative linguistics that constrains how far syntactic elements can move in a sentence.
-
B.
Bounds
Bounds is the maiden surname of Lillian Disney, the wife of Walt Disney and a key figure in the early Disney family history.
-
C.
Amdahl's law
Amdahl's law is a formula in computer architecture and parallel computing that predicts the maximum performance improvement achievable by parallelizing parts of a system, given that some portion must remain serial.
-
D.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
E.
Stirling's approximation
Stirling's approximation is a classical formula in mathematics that provides an efficient asymptotic estimate for factorials and the gamma function, especially for large arguments.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
asymptotic notation
ⓘ
complexity analysis tool ⓘ mathematical notation ⓘ |
| alsoKnownAs | O-notation ⓘ |
| appliedIn |
algorithm design
ⓘ
computational complexity theory ⓘ data structure analysis ⓘ performance engineering ⓘ |
| assumes | sufficiently large input size ⓘ |
| basedOn | asymptotic analysis ⓘ |
| characterizes |
upper bound on growth rate of a function
ⓘ
worst-case complexity of an algorithm ⓘ |
| commonExample |
O(1)
ⓘ
O(2^n) ⓘ O(log n) ⓘ O(n log n) ⓘ O(n!) ⓘ O(n) ⓘ O(n^2) ⓘ |
| compares |
growth of memory usage to input size
ⓘ
growth of running time to input size ⓘ |
| contrastsWith |
average-case analysis when used for worst-case bounds
ⓘ
exact running time measurement ⓘ |
| describes |
asymptotic upper bound ignoring constant factors
ⓘ
asymptotic upper bound ignoring lower-order terms ⓘ |
| field |
computer science
ⓘ
mathematics ⓘ |
| formalDefinitionInvolves |
existence of positive constants c and n0
ⓘ
inequality |f(n)| ≤ c·g(n) for all n ≥ n0 ⓘ |
| helpsWith |
choosing algorithms for large-scale problems
ⓘ
predicting algorithm performance for large inputs ⓘ |
| ignores |
constant-time differences
ⓘ
machine-dependent constants ⓘ |
| originatedIn | mathematical analysis ⓘ |
| relatedTo |
Big-Omega notation
ⓘ
Big-Theta notation ⓘ Landau notation ⓘ little-o notation ⓘ little-omega notation ⓘ |
| symbol | O ⓘ |
| taughtIn |
data structures courses
ⓘ
introductory algorithms courses ⓘ theoretical computer science courses ⓘ |
| usedFor |
analyzing scalability of algorithms
ⓘ
comparing algorithm efficiency ⓘ describing algorithm space complexity ⓘ describing algorithm time complexity ⓘ describing growth rates of functions ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Big-O notation Description of subject: Big-O notation is a mathematical tool used in computer science to describe how the running time or space requirements of an algorithm grow relative to the size of its input.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Big-O notation
linked to: Big-O notation