Homework 2

[Note: this webpage last modified Tuesday, 08-Feb-2011 21:19:01 EST]

This homework assignment is due before class starts on Tuesday, February 1. Your solutions should be explained in complete sentences such that your classmates will understand the solution (and can verify your proofs are correct) even if they have not solved the problems themselves.

  1. HW Polices.

    1. Type your HW (in word, latex, text file, etc.) and send to me by email.

    2. Do NOT share electronically. You must type your own solutions. You can discuss the problems with each other, but you may only discuss them. You may not write out solutions together.

    3. You MAY NOT search the Internet, textbooks, etc. for solutions to the problems. The following are the ONLY sources of information that you may use in solving the problems: the textbook for this course, wikipedia articles on basic math/probability/etc., and mathematical review material at the following MIT opencourseware page: 6.042J / 18.062J Mathematics for Computer Science, Fall 2005. You may discuss the problems with each other and with myself, but must obey the previous item in doing so.

      If you do find the solution in one of these three sources, you still MUST cite the source in your document.

      You may use NOTHING ELSE that is online or other textbooks.

    4. You MAY NOT copy word-for-word from any source, even the three you are allowed to consult. If you feel it is necessary, you should put the quotation in quotes and provide a reference/citation.

  2. (-2 points if left blank) List who you collaborated with on this assignment, "none" if none.

  3. Undecidability question has been moved to hw3.

  4. (10 Points) Find a problem that is NP-complete which we have not covered in class and is not given in the book. Give a proof that the problem is not decidable that takes less than one or two pages. You may consult any source for this problem, but you may not copy word for word, and you must cite the source. When you are typing your solution, you should not have your source in front of you. You can reserve a problem by emailing me. You will present your solution for this problem or the previous problem after the assignment is turned in.

    Problems chosen: subset sum (Subu, see Sipser text Introduction to the Theory of Computation for the proof), 3-coloring (Prudhvi, proof), vertex cover (Kartheek), Hamiltonian path (Nihar, see Sipser for the proof), clique (Bharat), exact cover (Derrick, source for proof, another source), traveling salesperson (Masood, proof), asymmetric split and symmetric split (Vijay), subgraph isomorphism (Chandana, proof), min cut (Sujana),

  5. (Extra Credit, 2 Points) Remember the Karp-reduction from 3-SAT to independent set. It is in the book, and we went over it in class. For this problem, pick your favorite programming language and actually implement the reduction. That is, start with a 3-SAT formula as input to the program, and then convert it into an instance of independent set.