Question 1

Consider a minimal spanning tree problem in which pipe must be laid to connect sprinklers on a golf course. When represented with a network,

Accepted Answer

A) the pipes are the arcs and the sprinklers are the nodes. 
B) the pipes are the nodes and the sprinklers are the arcs. 
C) the pipes and the sprinklers are the tree. 
D) each sprinkler must be connected to every other sprinkler. 
A) the pipes are the arcs and the sprinklers are the nodes. 
B) the pipes are the nodes and the sprinklers are the arcs. 
C) the pipes and the sprinklers are the tree. 
D) each sprinkler must be connected to every other sprinkler. A

Question 2

The minimal spanning tree algorithm will lead to an optimal solution regardless of which node is chosen at the start of the algorithm.

Accepted Answer

A) True 
 B)False  True

Question 3

For the following eight cities with the given distances, find the minimal spanning tree path. $$\begin{array} { c | c c c c c c c } 
& && { \text { To City } } \
\text { From City } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline 1 & - & 5 & 2 & 6 & - & - & - \
2 & 5 & - & - & 4 & 6 & - & - \
3 & 2 & - & - & 3 &- & 12 & -\4 & 6 & 4 & 3 & - & 9 & 8 & - \
5 & - & 6 & - & 9 & - & 0 & 14 \
6 & - & - & 12 & 8 & 0 & - & 4 \
7 & - & - & - & - & 14 & 4 & -\
\end{array}$$

Accepted Answer

1-3-4-2-5-6-7

Question 4

It is possible for minimal spanning tree problems to have alternative optimal solutions.

Accepted Answer

A) True 
 B)False

Question 5

The minimum spanning tree allows a person to visit every node without backtracking.

Accepted Answer

A) True 
 B)False

Question 6

The minimal spanning tree algorithm has connected nodes 8 and 9. Node 8 could be connected to nodes 11 (distance 6) and 12 (distance 5) and node 9 could be connected to node 12 (distance 3) and node 13 (distance 2). Which will you do next?

Accepted Answer

A) connect 8 to 11 
B) connect 8 to 12 
C) connect 9 to 12 
D) connect 9 to 13 
A) connect 8 to 11 
B) connect 8 to 12 
C) connect 9 to 12 
D) connect 9 to 13

Question 7

The minimum spanning tree algorithm is considered a heuristic.

Accepted Answer

A) True 
 B)False

Question 8

Find the minimal spanning tree for this network.

Accepted Answer

The answer of Find the minimal spanning tree for this...

Question 9

The minimal spanning tree algorithm is considered to be:

Accepted Answer

A) a greedy algorithm. 
B) an arc algorithm. 
C) a non-optimal algorithm. 
D) a non-feasible algorithm. 
A) a greedy algorithm. 
B) an arc algorithm. 
C) a non-optimal algorithm. 
D) a non-feasible algorithm.

Question 10

The minimal spanning tree algorithm will:

Accepted Answer

A) sometimes fail to produce a feasible solution. 
B) always produce a feasible, but not necessarily optimal, solution. 
C) always produce an optimal solution. 
D) always produce an optimal, but not necessarily feasible, solution. 
A) sometimes fail to produce a feasible solution. 
B) always produce a feasible, but not necessarily optimal, solution. 
C) always produce an optimal solution. 
D) always produce an optimal, but not necessarily feasible, solution.

Question 11

For a network consisting of N nodes, a minimal spanning tree will consist of:

Accepted Answer

A) N -2 arcs. 
B) N -1 arcs. 
C) N arcs. 
D) N + 1 arcs. 
A) N -2 arcs. 
B) N -1 arcs. 
C) N arcs. 
D) N + 1 arcs.

Question 12

Find the minimal spanning tree for this network.

Accepted Answer

The answer of Find the minimal spanning tree for this...

Question 13

What are some other criteria (measures), besides distance, that might be minimized in a minimal spanning tree problem? Provide an example situation for each criterion.

Accepted Answer

In addition to distance, there are sever

Question 14

The arcs in a minimal spanning tree problem can be measured in terms of criteria other than distance.

Accepted Answer

A) True 
 B)False

Question 15

Cases in which a greedy algorithm provides the optimal solution are rare.

Accepted Answer

A) True 
 B)False

Question 16

The numbers on this network represent times to distribute a message. Use the minimal spanning tree algorithm to determine how messages should be passed in order to minimize total time.

Accepted Answer

The answer of The numbers on this network represent times...

Question 17

In the minimal spanning tree algorithm, you must consider the unconnected nodes that can be reached from any of the connected nodes, rather than arbitrarily considering only one of the connected nodes.

Accepted Answer

A) True 
 B)False

Question 18

What is a greedy algorithm? What is an example of a greedy algorithm?

Accepted Answer

A greedy algorithm is a simple, intuitiv

Consider a minimal spanning tree problem in which pipe must be laid to connect sprinklers on a golf course. When represented with a network,

The minimal spanning tree algorithm will lead to an optimal solution regardless of which node is chosen at the start of the algorithm.

For the following eight cities with the given distances, find the minimal spanning tree path. To City From City 1 2 3 4 5 6 7 1 - 5 2 6 - - - 2 5 - - 4 6 - - 3 2 - - 3 - 12 - 4 6 4 3 - 9 8 - 5 - 6 - 9 - 0 14 6 - - 12 8 0 - 4 7 - - - - 14 4 -

It is possible for minimal spanning tree problems to have alternative optimal solutions.

The minimum spanning tree allows a person to visit every node without backtracking.

The minimal spanning tree algorithm has connected nodes 8 and 9. Node 8 could be connected to nodes 11 (distance 6) and 12 (distance 5) and node 9 could be connected to node 12 (distance 3) and node 13 (distance 2). Which will you do next?

The minimum spanning tree algorithm is considered a heuristic.

Find the minimal spanning tree for this network.

The minimal spanning tree algorithm is considered to be:

The minimal spanning tree algorithm will:

For a network consisting of N nodes, a minimal spanning tree will consist of:

Find the minimal spanning tree for this network.

What are some other criteria (measures), besides distance, that might be minimized in a minimal spanning tree problem? Provide an example situation for each criterion.

The arcs in a minimal spanning tree problem can be measured in terms of criteria other than distance.

Cases in which a greedy algorithm provides the optimal solution are rare.

The numbers on this network represent times to distribute a message. Use the minimal spanning tree algorithm to determine how messages should be passed in order to minimize total time.

In the minimal spanning tree algorithm, you must consider the unconnected nodes that can be reached from any of the connected nodes, rather than arbitrarily considering only one of the connected nodes.

What is a greedy algorithm? What is an example of a greedy algorithm?

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance and Operations Management

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Dynamic Programming

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Exam 20: Minimal Spanning Tree

Consider a minimal spanning tree problem in which pipe must be laid to connect sprinklers on a golf course. When represented with a network,

The minimal spanning tree algorithm will lead to an optimal solution regardless of which node is chosen at the start of the algorithm.

For the following eight cities with the given distances, find the minimal spanning tree path. To City From City 1 2 3 4 5 6 7 1 - 5 2 6 - - - 2 5 - - 4 6 - - 3 2 - - 3 - 12 - 4 6 4 3 - 9 8 - 5 - 6 - 9 - 0 14 6 - - 12 8 0 - 4 7 - - - - 14 4 -

It is possible for minimal spanning tree problems to have alternative optimal solutions.

The minimum spanning tree allows a person to visit every node without backtracking.

The minimal spanning tree algorithm has connected nodes 8 and 9. Node 8 could be connected to nodes 11 (distance 6) and 12 (distance 5) and node 9 could be connected to node 12 (distance 3) and node 13 (distance 2). Which will you do next?

The minimum spanning tree algorithm is considered a heuristic.

Find the minimal spanning tree for this network.

The minimal spanning tree algorithm is considered to be:

The minimal spanning tree algorithm will:

For a network consisting of N nodes, a minimal spanning tree will consist of:

Find the minimal spanning tree for this network.

What are some other criteria (measures), besides distance, that might be minimized in a minimal spanning tree problem? Provide an example situation for each criterion.

The arcs in a minimal spanning tree problem can be measured in terms of criteria other than distance.

Cases in which a greedy algorithm provides the optimal solution are rare.

The numbers on this network represent times to distribute a message. Use the minimal spanning tree algorithm to determine how messages should be passed in order to minimize total time.

In the minimal spanning tree algorithm, you must consider the unconnected nodes that can be reached from any of the connected nodes, rather than arbitrarily considering only one of the connected nodes.

What is a greedy algorithm? What is an example of a greedy algorithm?

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance and Operations Management

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Dynamic Programming

Filters