Data Structures and Algorithms

   

Efficiently Solving Traveling Salesman Problem in a Computer Network. (Internet)

Authors: Oscar E. Chamizo Sánchez

Traveling salesman problem (TSP for short) is perhaps the most widely known and deeply investigated problem in computation. Given a set of cities, the simple goal is to find the cheapest way of visiting all cities and returning to the starting one. The optimal (in case of a simetric euclidean TSP the shortest) path from the starting city to itself through all the remaining cities is, in general, only one from the (n-1)!/2 set of possible tours or circuits. In our seminal paper A new approach: A hardware device model solving TSP in O(n2) time we presented a physically realizable computation model solving any instance of TSP in O(n2) time, a model that can´t be efficiently simulated by a single TM, thus proving the fallacy of the so called strong form of Church-Turing thesis. In this paper we present a model of network computation that solves TSP in O(n2) time, model that could be implemented with some technical adjustments in a global system like internet. This network with five billions interconnected devices provides boundless possibilities in order to solve unprecedented instances of the TSP and therefore of other NP problems. In section 1 we go directly to the device model and prove mathematically its validity. In section 2 we explain the basic ideas behind the physical model. In section 3 we outline the key aspects to put into practice the theoretical model in a computer network.

Comments: 4 Pages.

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Submission history

[v1] 2018-04-28 04:57:56

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