NP-complete problems refer to decision problems.
Eg: set cover problem. The decision version of set covering is NP-complete, and the optimization version of set cover is NP-hard.
http://en.wikipedia.org/wiki/Set_cover_problem
Why the reduction started from CIRCUIT-SAT?
is CIRCUIT-SAT meaningful? useful?
The concept of NP-complete was introduced by Stephen Cook(Turing receiver)in 1971. In 1972, Richard Karpg (Turing receiver) proved that several other problems were also NP-complete (see Karp's 21 NP-complete problems);
Dominating Set Problem:
http://en.wikipedia.org/wiki/Dominating_set_problem
Karp's 21 NP-complete problems:
http://en.wikipedia.org/wiki/Karp's_21_NP-complete_problems
List of NP-complete problems:
http://en.wikipedia.org/wiki/List_of_NP-complete_problems
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