0) Use the nearest-neighbor algorithm starting with vertex C to find a Hamilton circuit.
0) Use the nearest-neighbor algorithm starting with vertex C to find a Hamilton circuit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Problem:**
Use the nearest-neighbor algorithm starting with vertex C to find a Hamilton circuit.
**Diagram Explanation:**
The diagram is a weighted graph consisting of four vertices: A, B, C, and D. They are connected by edges, each with an assigned weight representing the distance or cost between vertices:
- The edge between A and B has a weight of 9.
- The edge between A and C has a weight of 4.
- The edge between A and D has a weight of 5.
- The edge between B and C has a weight of 2.
- The edge between B and D has a weight of 8.
- The edge between C and D has a weight of 1.
The task is to apply the nearest-neighbor algorithm, starting at vertex C, to determine a Hamilton circuit that visits each vertex exactly once and returns to the starting vertex, C.
**Nearest-Neighbor Algorithm Steps:**
1. Start at vertex C.
2. Select the edge with the smallest weight connected to C. This is the edge C-D with a weight of 1.
3. Move to vertex D.
4. From D, select the next smallest edge to an unvisited vertex. This is the edge D-A with a weight of 5.
5. Move to vertex A.
6. From A, select the next smallest edge to an unvisited vertex. This is the edge A-B with a weight of 9.
7. Move to vertex B.
8. Finally, return to the starting vertex C, through the edge B-C with a weight of 2.
**Resulting Hamilton Circuit:**
C → D → A → B → C
The total weight of this circuit is 1 + 5 + 9 + 2 = 17.
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