the travelling sales person problem is to find the shortest tour

a tour visits every vertex and returns to the start vertex and will always have the same number of edges as there are nodes. For the following algorithms to be correct the graph must be complete if this is not the case the graph must be made complete first.

Nearest neighbour algorithm -calculating upper bounds

- from your start vertex go to nearest unvisited vertex
- from current vertex got to nearest unvisited vertex
- repeat previous step until all vertexes have been visited
- return to start vertex

remember the lowest upper bound is the best upper bound

calculating lower bounds

- delete a vertex and all connected edges
- find a minimum spanning tree for the remaining graph
- add the two shortest edges from the deleted vertex

remember the lower bound may not be possible and the highest lower bound is the best

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