UMBC CMSC641, Design & Analysis of Algorithms, Spring 2001
Homework Assignments
Homework is due the Tuesday after the work is assigned.
Remember that you are allowed to turn in up to 4 homework assignments late,
but they should not be more than 1 week late in any case.
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.
Homework 6, due 03/13/01.
Exercise 27.2-8, page 600.
Exercise 27.2-9, page 600.
Problem 27-1, page 625.
Homework 7, due 04/03/01.
Exercise 30.1-1, page 700.
Exercise 30.1-3, page 700.
Problem 30-1, page 726.
Homework 8, due 04/10/01.
Exercise 28.1-2, page 638.
Exercise 28.4-3, page 648.
Exercise 28.5-4, page 650.
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.
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