arXiv subjects

Mark H. Karwan

Publications and source records attributed to Mark H. Karwan.

2 recordsLinked to original sources

arXiv2019

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

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.

cs.CC↗

arXiv2016

On "Exponential Lower Bounds for Polytopes in Combinatorial Optimization" by Fiorini et al. (2015): A Refutation For Models With Disjoint Sets of Descriptive Variables

We provide a numerical refutation of the developments of Fiorini et al. (2015)* for models with disjoint sets of descriptive variables. We also provide an insight into the meaning of the existence of a one-to-one linear map between solutions of such models. *: Fiorini, S., S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf (2015). Exponential Lower Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM 62:2, Article No. 17.

cs.CC↗