CS517 Homework 2

Due May 1, 2:00 P.M.

All the numbers are from Arora & Barak.

2.2.
2.4.
2.9.
2.10.
2.14.
2.15.
2.21. For this problem, you are allowed to refer to the web and other sources. Try it first on your own. Write a brief summary of the answer *in your own words* citing any sources you referenced.
2.26.

Define MaxSAT as follows:
Given a CNF formula and an integer K, does there exist an assignment that satisfies at least K clauses? Show that MaxSAT is NP-complete.

Integer programming is defined as follows:
Given a set of m linear inequalities over variables u1,...un, with rational coefficients, find out if there is an assignment of integers to u1,...,un that satisfies all inequalities. Show that integer programming as defined above is NP-hard.