An electronic algorithm to find the optimal solution for the travelling salesman problem

Mohamed Sghiar (1)

1 Chercheur indépendant

Abstract: I give here an electronic algorithm of the order $ \mathcal{ O } (n ^ 3 ) $ which is a generalization of the atomic algorithm found in [6] and allows us to find the optimal hamiltonian cycles. If the atomic algorithm (see [6] and [5] ) was inspired by the movement of the particles in the atom, the electronic algorithm is inspired by the resistor in the electrical circuit.

Mots clés: Graph; Hamilton cycles; P=NP; the travelling salesman problem; TSP.

Domaines: Combinatoire [math.CO]; Complexité [cs.CC]; Informatique et langage [cs.CL]; Théorie de l'information [cs.IT]; Mathématique discrète [cs.DM]; Langage de programmation [cs.PL]; Logique [math.LO]

Mohamed Sghiar. An electronic algorithm to find the optimal solution for the travelling salesman problem. IOSR Journal of Mathematics(IOSR-JM), 2016, 12 (Issue 4), pp.82-86. ⟨hal-01353706⟩