Worst case of nearest neighbor heuristic for symmetric TSP

Question

I have implemented the nearest neighbor heuristic for solving symmetric TSP problems. I was wondering if there is any relation between the solution found by the heuristic and the optimal solution?

Can we state theoretically how much higher the route length is in a worst case scenario?

score 1 · Answer 1 · answered Nov 18 '13 at 11:04

1

The book "In pursuit of the Traveling Salesman" (Cook) mentions that: nearest neighbor will never do worse than 1 + log(n)/2 times the cost of the optimal (which in turn comes from some paper).

It's a great book, described the other construction heuristics too.

answered Nov 18 '13 at 11:04

Geoffrey De Smet

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Do note that TSP is simple: it doesn't have many constraints, nor any difficult ones. In real world cases (VRP variants etc), the gap is far wider. – Geoffrey De Smet Nov 18 '13 at 11:05
Does this also apply to symmetric TSP that NOT satisfy the triangle inequality? – user19553 Nov 20 '13 at 09:20

Worst case of nearest neighbor heuristic for symmetric TSP

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