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CSE 830: Design and Theory of Algorithms
Homework #5
Due Monday, April 21
st
2008, 3pm
Each problem should be solved on a separate sheet of paper to facilitate grading. Limit the
solution of each problem to one sheet of paper. Please don't wait until the last minute to look at
the problems.
1.
The
Graphisomorphism problem
is an open problem; no one has yet been able to prove it to
be a hard problem, yet no polynomial time algorithm has been constructed either. Show that
Graph Isomorphism is in NP by describing what certificate should be returned with a “yes”
answer, and how that certificate can be verified in polynomial time. Analyze the time
complexity for this verification.
2.
The
Subgraphisomorphism problem
is much easier to deal with than its fullgraph
counterpart. This problem takes two graphs G
1
and G
2
and asks whether G
1
can be found as a
subgraph in G
2
. Show that the subgraphisomorphism problem is NPcomplete.
3.
Implement
an algorithm to solve the
vertex cover
problem. To do this, use the Minimum
Dominating Set program implemented by one of your group members. Write only two
additional sections in your program: one to preprocess the input graph to run under the
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 Spring '08
 OFRIA
 Algorithms

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