Deck 20: Minimal Spanning Tree

Question 1

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

Answer 1

True

Question 2

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 of the following will you do next?

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

Answer 2

D

Question 3

Find the minimal spanning tree for this network.​

Answer 3

​

Question 4

Find the minimal spanning tree for this network.​

Question 5

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 6

A minimal spanning tree problem involves using the arcs of the network to reach all nodes of the network such that the total length of all the arcs used is maximized.

Question 7

The minimal spanning tree algorithm is considered a greedy algorithm that,when taking the best action at each stage,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.

Question 8

Ethernet cable costs $25 per foot to install.The table below gives the approximate direct routing distance in feet between various pairs of machines.​ ​
a.Use the minimal spanning tree algorithm to determine the least cost method of connecting all machines.
b.How much cheaper would it be if the company decided not to hook up the second printer to this system?

Question 9

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

Question 10

The minimal spanning tree algorithm is considered to be a(n)

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

Question 11

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

Question 12

Griffith's Cherry Preserve is a combination wild animal habitat and amusement park.Besides its phenomenally successful wild animal safari tour,there are eight different theme areas in the amusement park.​
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.​
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.​

Question 13

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 14

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

Question 15

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.​

Question 16

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 17

For a network consisting of N nodes,a spanning tree will consist of N - 1 arcs.

Question 18

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

Question 19

Cases in which a greedy algorithm provides the optimal solution are rare,but greedy algorithms are excellent heuristics.