This preview shows page 1. Sign up to view the full content.
CSE 830: Design and Theory of Algorithms
Homework #4
Due Monday, March 17
th
2008, 3pm
1.
Is the path between a pair of vertices in a minimum spanning tree necessarily the shortest path
between the two vertices in the full graph? Give a proof or a counterexample.
2.
Suppose G is a connected undirected graph. An edge
e
whose removal disconnects the graph is
called a
bridge
. Must every bridge
e
be an edge in a depthfirst search tree of G, or can e be a back
edge? Give a proof or a counterexample.
3.
In breadthfirst and depthfirst search, an
undiscovered
node is marked
discovered
when it is first
encountered, and marked
completelyexplored
when it has been fully searched. At any given
moment, various numbers of nodes can be in any of these states. In all cases below, describe a
graph on n vertices with a particular starting vertex
v
that has the properties described.
a.
At some point during a breadthfirst search,
Θ
(
n
) are simultaneously in the discovered state.
b.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/25/2008 for the course CSE 830 taught by Professor Ofria during the Spring '08 term at Michigan State University.
 Spring '08
 OFRIA
 Algorithms

Click to edit the document details