- Homework 1, due 02/06/01.
- Homework 2, due 02/13/01.
- Homework 3, due 02/20/01.
- Homework 4, due 02/27/01.
- Exercise 21.4-1, page 438.
- Problem 21-2, page 439.
- Problem 22-1, page 458.

- Homework 5, due 03/06/01.
- Exercise 22.3-4, page 450.

Note: where the question mentions the UNION operation, replace it with the LINK operation. - Problem 22-3, page 460.

- Exercise 22.3-4, page 450.
- Homework 6, due 03/13/01.
- Exercise 27.2-8, page 600.

- Exercise 27.2-9, page 600.

- Problem 27-1, page 625.

- Exercise 27.2-8, page 600.
- Homework 7, due 04/03/01.
- Exercise 30.1-1, page 700.

- Exercise 30.1-3, page 700.

- Problem 30-1, page 726.

- Exercise 30.1-1, page 700.
- Homework 8, due 04/10/01.
- Exercise 28.1-2, page 638.

- Exercise 28.4-3, page 648.

- Exercise 28.5-4, page 650.

- Exercise 28.1-2, page 638.
- Homework 9, due 04/17/01.
- Exercise 6.3-3, page 114.
- Exercise 6.4-2, page 119.
- Consider the following modification to the randomized
MinCut algorithm presented in class. Instead of choosing a
random edge for contraction, choose two vertices at random
and merge them into a single vertex. Here the two vertices do
not have to be connected by an edge. Show that there are inputs
on which the probability that this modified algorithm finds
a min-cut is exponentially small.
[Exercise 1.2,
*Randomized Algorithms*, Motwani and Raghavan.]

- Homework 10, due 04/24/01.
- Exercise 35.1-3, page 891.

(Hint: think about Exercise 35.1-2.) - Exercise 35.1-5, page 891.
- Exercise 35.2-6, page 898.

- Exercise 35.1-3, page 891.
- Homework 11, due 05/01/01.
- Exercise 35.3-6, page 908.
- Exercise 35.4-1, page 912.
- Exercise 35.4-4, page 912.

- Homework 12, due 05/08/01.
- Exercise 36.5-2, page 960.
- Exercise 36.5-5, page 961.
- Prove that 3-colorability for planar graphs is NP-complete. (You may assume that 3-colorability for general graphs is NP-complete.)

- Homework 13, due 05/15/01.
- Exercise 36.2-3, page 928.
- Exercise 36.5-4, page 960.
- Prove that Steiner Tree on Graphs (STG) is NP-complete.
(
*Hint:*reduce from 3DM.)STG = { (G,R,k) | where G=(V,E) is an undirected graph, R is a subset of V and k <= |V|-1 such that there exists a subtree T of G that includes all the vertices of R and T contains no more than k edges.}

Last Modified: 8 May 2001 17:38:28 EDT by

Richard Chang

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