CSOR 4231 05F: Homework 7

Required for Undergraduates: 6 of the following 9 problems
Required for Graduate Students: 7 of the following 9 problems
Points: 10 pts per problem

General Instructions

1. Please review the homework and grading policy outlined in the course information page.

2. On the first page of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

   Problem	01	02	03	04	05	06	07	08	09	...
   Credit	RC	RC	RC	EC	RC	RC	NA	RC	RC	...

   where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not attempted" (not applicable). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
4. Start early, be concise but rigorous, and enjoy!

Specific Instructions

1. Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.

Problems

1. Exercise 25.1-1. Shortest paths via matrix multiplication.
2. Exercise 25.2-5. Floyd-Warshall.
3. Exercise 34.2-5. Algorithm for NP-problem. Replace the word "language" with "problem".
4. Exercise 34.4-6. Self-reducibility. Remember that "a polynomial-time algorithm to decide formulate satisfiability" is an algorithm that just outputs "yes" or "no", indicating whether a formula is satisfiable.
5. Exercise 34.5-1. Subgraph isomorphism is NP-complete.
6. Problem 34.3. Graph coloring.
7. Problem 34.1 Independent set.
8. Exercise 35.1-3. Vertex cover.
9. Problem 35-5. Parallel machine scheduling.

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