Deck 20: Minimal Spanning Tree

Question 1

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 1

A

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

The minimum spanning tree algorithm is considered a heuristic.

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

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

Question 9

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.

Question 10

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

Question 11

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 12

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.