CS 473
Homework 10 (practice only)
Spring 2010
This homework is practice only. However, there will be at least one NPhardness problem
on the final exam, so working through this homework is
strongly
recommended.
Stu
dents
/
groups are welcome to submit solutions for feedback (but not credit) in class on May
4, after which we will publish official solutions.
1.
Recall that 3SAT asks whether a given boolean formula in conjunctive normal form, with exactly
three literals in each clause, is satisfiable. In class we proved that 3SAT is NPcomplete, using a
reduction from C
IRCUIT
SAT.
Now consider the related problem
2SAT
: Given a boolean formula in conjunctive normal form,
with exactly
two
literals in each clause, is the formula satisfiable? For example, the following
boolean formula is a valid input to 2SAT:
(
x
∨
y
)
∧
(
y
∨
z
)
∧
(
x
∨
z
)
∧
(
w
∨
y
)
.
Either prove that 2SAT is NPhard or describe a polynomialtime algorithm to solve it.
[Hint:
Recall that
(
x
∨
y
)
≡
(
x
→
y
)
, and build a graph.]
2.
Let
G
= (
V
,
E
)
be a graph. A
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 Spring '08
 Chekuri,C
 Algorithms, Computational complexity theory, Conjunctive normal form, Dominating set, NPcomplete, Boolean formula, 3SAT

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