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W08/CS5592
Homework Four
Design and Analysis of Algorithms
Due: Monday, March 31, 2008, in class
There are four problems
1 (a)
Conduct a DFS for the following graph. Please label each vertex
u
with the
discovery time and the finish time
d
(
u
)/
f
(
u
). You should start the traversal from
vertex
a
, and follow the alphabetic order whenever you need to make choices.
p
e
f
h
a
s
d
g
b
c
k
m
j
(b)
List all edges that belong to each of the following sets:
The set of tree (or forest) edges:
The set of back edges:
The set of forward edges:
The set of cross edges:
(c)
Identify the strongly connected components and draw the component graph.
1
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An
independent set
of a graph G = (V, E) is a subset V’
⊆
V of vertices such that
each edge in E is incident on at most one vertex in V’. The
independentset problem
is to find a maximumsize independent set in G. This is a difficult problem for general
graph G. We will discuss in Chapter 34. However it is not difficult if G is a tree.
Let T be a tree. Please design an efficient algorithm to find a maximumsize
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This note was uploaded on 04/12/2008 for the course CS 592 taught by Professor Shen during the Winter '05 term at University of MissouriKansas City .
 Winter '05
 Shen
 Algorithms

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