CS 466/666

Monday October 29

To sign up for a problem, send email to alubiw "at" uwaterloo.ca. I will update this list to indicate the first person who signs up.
  1. [Thomas Ang] (from lecture 13) Show that RP \subset NP. (Part of the presentation should be to explain RP and NP again. Also explain why you can't easily show NP \subset RP.)

  2. [Can Tang] (from lecture 13) Show ZPP = RP intersect coRP.

  3. [Yin Zhao] (from lecture 14) Prove: Let f(x_1, . . . , x_n) be a multivariate polynomial of total degree d. Suppose that f is not identically 0 and that values a_1, . . . , a_n are drawn independently and uniformly from a finite set S. Then Prob{f(a_1, . . . , a_n) = 0} <= d / |S|.

  4. [Andrei Barbu] Formulate the following problem as a 2 dimensional linear program: Given a set of points in the plane, find the best line fitting the points, where "best" means minimize the maximum vertical distance of a point from the line. If time, consider other objective functions, e.g. minimize the sum of vertical distances of points to the line.

  5. [Ahren Langschmidt] Give a polynomial time algorithm for 2-SAT (a deterministic algorithm).