CSE 200
Computability and Complexity
Homework 2
NP, Completeness, and Reductions
Due Monday, May 10
April 26, 2010
Give proofs for each problem. Proofs can be highlevel, but be precise. You
may use without giving a proof any result proved in class or in the textbook. In
particular, to prove NPcompleteness, it suffices to give a reduction from any of
the NPcomplete problems from the text or from class. However, you must show
your reduction is valid, by showing the equivalence of the constructed instance
and the original.
Restricted 3SAT Show that the 3SAT problem remains
NP
complete when restricted to
formulas where each variable appears at most 3 times. (Hint: remember
that you can use smaller clauses than size 3.)
Independent Set Maximality (ISM) Prove that the following problem is
NP
complete. Given a graph
G
and
an independent set
I
in
G
, is there a larger independent set
I
0
,

I

<

I
0

?
Abstract tiling Consider the abstract tiling problem shown noncomputable in class, but
where in addition to the set of tiles
T
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 Winter '12
 Edmonds
 NPcomplete, Boolean satisfiability problem, abstract sudoku problem

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