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.

1. Exercise 7.5 in Sipser
2. Exercise 7.6 in Sipser
3. Exercise 7.7 in Sipser
4. Exercise 7.12 in Sipser
5. Exercise 7.23 in Sipser
6. Define SUBGRAPH-ISOMORPHISM 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 one-to-one 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 SUBGRAPH-ISOMORPHISM is NP-complete.
7. Define INDEPENDENT-SET 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 INDEPENDENT-SET is NP-complete.
8. Define HYPER-COMMUNITY 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 HYPER-COMMUNITY is NP-complete.
9. Exercise 8.4 in Sipser