CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 6: Graph Algorithms I
Due Date
: Nov. 12, 2004 (at the beginning of CSE 413 class)
Note
: We assume that all input graphs are based on the adjacency list representation (see page 84
of Manber’s book for the adjacency list representation of graphs).
1. Let
G
=(
V,E
) be an undirected graph of
n
vertices and
m
edges, such that every edge
e
of
E
has a weight
w
(
e
)
≥
0(
w
(
e
) is a real number). For any input integer
k>
0 and two vertices
s
and
t
of
G
,a
k
edge shortest path
in
G
is de±ned as follows: It is an
s
to
t
path in
G
that consists of
no more than
k
edges and that has the minimum total sum of edge weights
among all possible
s
to
t
paths in
G
with no more than
k
edges. Design an
O
(
k
(
m
+
n
)) time
algorithm based on the dynamic programming technique for computing a
k
edge shortest path
in
G
.
(
20 points
)
2. Recall the Hamiltonian
cycle
problem in Assignment 1 of this class. In this problem, you are
asked to solve the
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 Spring '11
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 Graph Theory, Analysis of algorithms, Hamiltonian path problem, adjacency list representation, time algorithm, kedge shortest path

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