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About: Extension complexity     Goto   Sponge   NotDistinct   Permalink

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In convex geometry and polyhedral combinatorics, the extension complexity is a convex polytope is the smallest number of facets among convex polytopes that have as a projection. In this context, is called an extended formulation of ; it may have much higher dimension than . The extension complexity depends on the precise shape of , not just on its combinatorial structure. For instance, regular polygons with sides have extension complexity (expressed using big O notation), but some other convex -gons have extension complexity at least proportional to .