A special case of this problem was solved using DNA oligonucleotides by Leonard Adelman. Other methods have included the Christofides algorithm and k-opt heuristic, but the first mathematical exposition of this problem was by Karl Menger, who knew that the na?e "nearest neighbor" heuristic solution was only optimal when the triangle inequality was 
A special case of this problem was solved using DNA oligonucleotides by Leonard Adelman. Other methods have included the Christofides algorithm and k-opt heuristic, but the first mathematical exposition of this problem was by Karl Menger, who knew that the na?e "nearest neighbor" heuristic solution was only optimal when the triangle inequality was satisfied. It can be solved exactly in some cases with the cutting plane method, and a specific instance based on 24,798 cities in Sweden has been solved, though an efficient general algorithm remains elusive. The bottleneck version is NP-hard, but the decision version of this problem can be shown to be NP-complete by a reduction to a Hamiltonian Path. FTP, identify this important problem in optimization, in which a hypothetical merchant must travel to each city once and then return home.
A special case of this problem was solved using DNA oligonucleotides by Leonard Adelman.
Traveling Salesman problem