Data Structures and Algorithms

   

A New Approach: a Hardware Device Model Solving TSP in O(n2) Time.

Authors: Óscar 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 this paper we present a hardware device model solving any instance of TSP in O(n2) time. 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 analyze complexity in such a device. In section 4 we outline the key aspects to put into practice the theoretical model in a feasible device. Finally in section 5 we discuss interesting implications in the field of computational complexity with special regard to the widely believed conjecture P≠NP.

Comments: 5 Pages.

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Submission history

[v1] 2018-03-17 04:27:47

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