assg-2作业

Design and Analysis of Algorithms (17 Spring)

Assignment 2

Due: Apr. 12, 2017

1. Please answer the following questions:

(a) What is polynomial reduction?

(b) What is the relation among P, NP and EXP?

(c) What are the main steps of proving the NP-Completeness of a problem?

2. Prove that: if we can check whether a graph has a clique (a complete graph) of size k in polynomial time then we can also find a clique of size k in polynomial time.

3. Compute a maximum flow from S to T in the following graph.

4. An edge set S in a graph is called an induced matching if no pair of edges in S have

a common endpoint or are adjacent by another edge. Please prove that finding an induced matching of size k in a graph is NP-Complete.