Exam 20: Minimal Spanning Tree

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

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 is considered to be a(n)

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.​

Find the minimal spanning tree for this network.​

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

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

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

Find the minimal spanning tree for this network.​

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

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.

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

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.​

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?

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

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?

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

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.

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