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

TL;DR

This paper critically examines Fiorini et al.'s 2015 results on polytope lower bounds in combinatorial optimization, providing a numerical refutation for models with disjoint descriptive variable sets and clarifying the implications of linear solution mappings.

Contribution

It offers a numerical refutation of prior exponential lower bounds for certain models, challenging the generality of Fiorini et al.'s conclusions.

Findings

Refutes Fiorini et al.'s exponential lower bounds numerically

Provides insights into linear mappings between models

Challenges assumptions about polytope complexity in combinatorial optimization

Abstract

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.