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Karp's 21 NP-complete problems
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Karp's 21 NP-complete problems
In
computational complexity theory
,
Karp's 21 NP-complete problems
are a set of
computational problems
which are
NP-complete
. In his 1972 paper, "Reducibility Among Combinatorial Problems",
Richard Karp
used
Stephen Cook
's 1971 theorem that the
boolean satisfiability problem
is
NP-complete
(also called the
Cook-Levin theorem
) to show that there is a
polynomial time
many-one reduction
from the boolean satisfiability problem to each of 21
combinatorial
and
graph theoretical
computational problems, thereby showing that they are all
NP-complete
. This was one of the first demonstrations that many natural computational problems occurring throughout
computer science
are
computationally intractable
, and it drove interest in the study of NP-completeness and the
P versus NP problem
.
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