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hw1 - CS 573 Graduate Algorithms Fall 2011 HW 1(due Tuesday...

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CS 573: Graduate Algorithms, Fall 2011 HW 1 (due Tuesday, September 13th) This homework contains five problems. Read the instructions for submitting homework on the course webpage . In particular, make sure that you write the solutions for the problems on separate sheets of paper. Write your name and netid on each sheet. Collaboration Policy: For this home work students can work in groups of up to three students each. Only one copy of the homework is to be submitted for each group. Make sure to list all the names/netids clearly on each page. Note on Proofs: Details are important in proofs but so is conciseness. Striking a good balance between them is a skill that is very useful to develop, especially at the graduate level. 1. (20 pts) Proofs are not necessary for the following two problems which should be easy reduc- tions from known problems. (10 pts) k -Bounded Set Cover is the special case of Set Cover in which the car- dinality of each set is at most k . Describe a reduction to show that 3 -Bounded Set Cover is NP-Hard. (10 pts) A directed graph G = ( V, E ) is strongly connected if for all u, v V there is a path in G from u to v and from v to u . The Strongly-Connected Spanning Subgraph
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