Deck 20: Minimal Spanning Tree

Question 1

​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.

Answer 1

​Answer not provided.

Question 2

The minimal spanning tree algorithm will:

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.

Answer 2

C

Question 3

The minimal spanning tree algorithm is considered to be:

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

Answer 3

A

Question 4

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.

Question 5

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

Question 6

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

Question 7

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

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

Question 8

​Describe three examples of minimal spanning tree problems.

Question 9

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?

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

Question 10

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

Question 11

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

Question 12

For the following eight cities with the given distances, find the minimal spanning tree path.

Question 13

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

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.

Question 14

The minimum spanning tree algorithm is considered a heuristic.

Question 15

Find the minimal spanning tree for this network.
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Question 16

Find the minimal spanning tree for this network.
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Question 17

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

Question 18

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.
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1. (River-1),(1-4),(4-6),(4-5),(6-7),(4-3),(3-8),(3-2).
2. (River-1),(1-4),(4-6),(4-5),(6-7),(4-3),(3-8),(4-2).
Total yards = 2050.
19. ​
Griffith's Cherry Preserve is a combination wild animal habitat and amusement park. Besides their phenomenally successful wild animal safari tour, there are eight different theme areas in the amusement park.
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One problem encountered by management is to develop a method by which people can efficiently travel between each area of the park. Management has learned that a people mover can be constructed at a cost of $50 per foot.
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If the following network represents the distances (in feet) between each area of the park for which a people mover is possible, determine the minimum cost for such a system.
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Question 19

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