On modeling hard combinatorial optimization problems as linear programs: Refutations of the "unconditional impossibility" claims

02/10/2019

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by   Moustapha Diaby, et al.

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University of Connecticut

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University at Buffalo

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There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial optimization problem in which the defining combinatorial configurations (such as "tours" in the case of the traveling salesman problem (TSP) for example) can be modeled by a polynomial-sized system of linear constraints. The purpose of this paper is to provide general as well as specific refutations for these recent claims.