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Ch5 NP Complete Problems
第 25 題／共 30 題
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AL 25/30
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25. NP-Complete、NP-Hard
#AL-05-025
中
NP-Complete
NP-Hard
📝
☆
Which of the following statements are necessarily true?
A
If a polynomial-time algorithm exists for the optimization version of an NP-complete problem, then the corresponding decision version is also solvable in polynomial time.
B
If a language
L
L
L
is NP-hard and
L
∈
c
o
N
P
L \in coNP
L
∈
co
N
P
, then
N
P
=
c
o
N
P
NP = coNP
N
P
=
co
N
P
.
C
There exists an NP-complete problem whose complement is also NP-complete.
D
If problem
A
A
A
is NP-complete and
A
≤
p
B
A \le_p B
A
≤
p
B
, then
B
B
B
is NP-complete.
E
If an NP-complete problem admits a polynomial-time approximation scheme (PTAS), then
P
=
N
P
P = NP
P
=
N
P
.
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