ICS 162  Final Exam Study Questions
The final exam
is comprehensive. Thus, the previous study
questions for
Midterm 1 and
Midterm 2 also apply to the final exam.
In addition to the readings and previous homeworks, listed on the
CS 162 Homework page,
and the previous study questions,
solving the following questions will provide a good preparation
for the final exam.
 Exercise 7.5 in Sipser
 Exercise 7.6 in Sipser
 Exercise 7.7 in Sipser
 Exercise 7.12 in Sipser
 Exercise 7.23 in Sipser

Define SUBGRAPHISOMORPHISM as the problem that takes a graph, G, and
another graph, H, and determines if H is isomorphic to a subgraph of G. That
is, the problem is to determine whether there is a onetoone mapping, f, of the
vertices in H to a subset of the vertices in G such that, if (v,w) is an edge in
H, then (f(v), f(w)) is an edge in G. Show that SUBGRAPHISOMORPHISM is
NPcomplete.

Define INDEPENDENTSET as the problem that takes a graph G and an integer k
and asks whether G contains an independent set of vertices of size k. That is, G
contains a set I of vertices of size k such that, for any v and w in I, there is no
edge (v,w) in G. Show that INDEPENDENTSET is NPcomplete.

Define HYPERCOMMUNITY to be the problem that takes a collection of n web
pages and an integer k, and determines if there are k web pages that all contain
hyperlinks to each other. Show that HYPERCOMMUNITY is NPcomplete.
 Exercise 8.4 in Sipser