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.

Download: PDF

Submission history

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

Unique-IP document downloads: 40 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus