An algebraic approach to symmetric extended formulations

Gábor Braun; Sebastian Pokutta

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arXiv · 1206.6318

An algebraic approach to symmetric extended formulations

Gábor Braun·Sebastian Pokutta

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Abstract

Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended formulation, i.e., one involving only a polynomial number of inequalities in its dimension. For the case of symmetric extended formulations (i.e., preserving the symmetries of the polytope) Yannakakis established a powerful technique to derive lower bounds and rule out small formulations. We rephrase the technique of Yannakakis in a group-theoretic framework. This provides a different perspective on symmetric extensions and considerably simplifies several lower bound constructions.

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Gábor Braun, Sebastian Pokutta. 2012-06-27. An algebraic approach to symmetric extended formulations. https://arxiv.org/abs/1206.6318

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