speedup theorem
E503602
The speedup theorem is a result in computational complexity theory showing that for certain problems, no single algorithm is asymptotically optimal because there always exists another algorithm that solves the problem significantly faster according to a given complexity measure.
All labels observed (3)
| Label | Occurrences |
|---|---|
| space speedup theorem | 1 |
| speedup theorem canonical | 1 |
| time speedup theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5213972 — 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: speedup theorem Context triple: [Blum complexity measures, relatedTo, speedup theorem]
-
A.
Accelerate
Accelerate is a song by the Christian rock band Liberation, known for its energetic style and uplifting, faith-centered lyrics.
-
B.
Speed
Speed is a 1994 action thriller film starring Keanu Reeves and Sandra Bullock, centered on a city bus that will explode if its speed drops below 50 miles per hour.
-
C.
SPEED
SPEED was an American cable and satellite television network focused on motorsports and automotive programming.
-
D.
Fastiv
Fastiv is a historic city in northern Ukraine known as a regional railway hub and industrial center southwest of Kyiv.
-
E.
Speedvision
Speedvision was a U.S. cable television network focused on motorsports and automotive programming, which later rebranded as Speed Channel.
- 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: speedup theorem Target entity description: The speedup theorem is a result in computational complexity theory showing that for certain problems, no single algorithm is asymptotically optimal because there always exists another algorithm that solves the problem significantly faster according to a given complexity measure.
-
A.
Accelerate
Accelerate is a song by the Christian rock band Liberation, known for its energetic style and uplifting, faith-centered lyrics.
-
B.
Speed
Speed is a 1994 action thriller film starring Keanu Reeves and Sandra Bullock, centered on a city bus that will explode if its speed drops below 50 miles per hour.
-
C.
SPEED
SPEED was an American cable and satellite television network focused on motorsports and automotive programming.
-
D.
Fastiv
Fastiv is a historic city in northern Ukraine known as a regional railway hub and industrial center southwest of Kyiv.
-
E.
Speedvision
Speedvision was a U.S. cable television network focused on motorsports and automotive programming, which later rebranded as Speed Channel.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf | theorem in computational complexity theory ⓘ |
| allows | construction of problems with arbitrarily large speedups between algorithms ⓘ |
| appliesTo |
computable functions
ⓘ
decision problems ⓘ |
| category |
non-constructive existence theorem in complexity theory
ⓘ
result about algorithmic optimality ⓘ |
| concerns |
complexity measures
ⓘ
time complexity ⓘ |
| contrastsWith | problems that have asymptotically optimal algorithms ⓘ |
| dependsOn | choice of complexity measure ⓘ |
| describes | existence of problems with no asymptotically optimal algorithm ⓘ |
| field |
computational complexity theory
ⓘ
theoretical computer science ⓘ
linked to:
Theoretical Computer Science
|
| hasConsequence |
complexity of some problems is not well-captured by a single algorithm
ⓘ
existence of problems whose optimal running time is not well-defined up to constant factors ⓘ |
| hasVariant |
space speedup theorem
ⓘ
linked to:
speedup theorem
time speedup theorem ⓘ
linked to:
speedup theorem
|
| implies |
for some problems there is an infinite sequence of increasingly faster algorithms
ⓘ
nonexistence of a single best algorithm for certain problems ⓘ there exist problems with arbitrarily large space speedups ⓘ there exist problems with arbitrarily large time speedups ⓘ |
| involvesConcept |
Turing machines
ⓘ
linked to:
Turing machine
asymptotic growth rates ⓘ complexity bounds ⓘ computable functions ⓘ partial recursive functions ⓘ |
| relatedTo |
Blum complexity axioms
ⓘ
linked to:
Blum axioms
algorithmic efficiency ⓘ asymptotic optimality of algorithms ⓘ complexity classes ⓘ space hierarchy theorem ⓘ time hierarchy theorem ⓘ |
| requires | a chosen complexity measure ⓘ |
| shows |
existence of problems with no optimal algorithm under certain measures
ⓘ
for some problems, any given algorithm is suboptimal by an unbounded factor ⓘ |
| states | for some problems and some complexity measures, every algorithm can be significantly improved upon ⓘ |
| usedInArgument |
limits of worst-case complexity as a practical guide
ⓘ
pathological nature of some complexity-theoretic constructions ⓘ |
| usesTechnique |
diagonalization
ⓘ
problem encoding tailored to a complexity measure ⓘ |
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: speedup theorem Description of subject: The speedup theorem is a result in computational complexity theory showing that for certain problems, no single algorithm is asymptotically optimal because there always exists another algorithm that solves the problem significantly faster according to a given complexity measure.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: speedup theorem
linked to: speedup theorem