BUS 31.4 Chapter 12 - Copy

BUS 31.4 Chapter 12 - Copy - 4. If all nodes are connected,...

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Chapter 12 – Network Models S. Neuburger Network Models Some basic graph theory terminology: Nodes (points) Edges / Arcs (lines) Isomorphism between seemingly different graphs (i.e., Petersen graph) Draw some classical graphs: path, star, wheel, cycle Path – sequence of nodes to traverse to get from start to end point Cycles – path that begins and ends at the same node Unconnected vs. Connected graphs Tree is a graph that has no cycles (minimum number of edges to maintain connectedness) Minimal Spanning Tree Goal: Connect all the points of a network while minimizing the distance covered. 1. Select any node 2. Connect this node to its nearest neighbor (minimum distance) 3. Find the nearest node to the connected set of nodes and connect it.
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Unformatted text preview: 4. If all nodes are connected, stop. Otherwise continue with step 3 iteratively. (This is Prims algorithm. Can also use Kruskals choose shortest edges while not getting cycle until all nodes are connected.) Shortest Route Goal: minimize total distance from source node to series of destination nodes. 1. Find the nearest node to origin. (Record distance in box near the node.) 2. Find the next-nearest node to origin. (Record distance in box near the node.) 3. Repeat until all nodes have been visited. The distance at the ending node is the length of the shortest route; the distance placed at each node is the shortest route to that node....
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