The fundamentality of the traveling salesman problem (TSP) is the choice of an edge in the next step. This paper proposes a concept of link degree, which can display the potentiality of an edge to belong to the shortest Hamiltonian cycle in a more effectively manner and, on this basis, it presents a greedy algorithm for the TSP. Meanwhile, some relevant theorems and conjectures as well as some problems triggered are discussed as well.

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In October 2010, a new British study said that bumblebees fluttering from flower to flower showed the ability to easily solve the “traveler salesman problem.” There is no good explanation for how the bumblebee solved the problem. In this paper, a simple and efficient algorithm is proposed to explain how bumblebee solves the traveling salesman problem.

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