
Extended formulations for matroid polytopes through randomized protocols
Let P be a polytope. The hitting number of P is the smallest size of a h...
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Extended formulations from communication protocols in outputefficient time
Deterministic protocols are wellknown tools to obtain extended formulat...
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Level Planarity: Transitivity vs. Even Crossings
Recently, Fulek et al. have presented HananiTutte results for (radial) ...
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Rational Radial Distortion Models with Analytical Undistortion Formulae
The common approach to radial distortion is by the means of polynomial a...
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An IntegerLinear Program for BendMinimization in OrthoRadial Drawings
An orthoradial grid is described by concentric circles and straightlin...
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Between steps: Intermediate relaxations between bigM and convex hull formulations
This work develops a class of relaxations in between the bigM and conve...
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A Comparison of Radial and Linear Charts for Visualizing Daily Pattern
Radial charts are generally considered less effective than linear charts...
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Extended Formulations for Radial Cones
This paper studies extended formulations for radial cones at vertices of polyhedra, where the radial cone of a polyhedron P at a vertex v ∈ P is the polyhedron defined by the constraints of P that are active at v . Given an extended formulation for P , it is easy to obtain an extended formulation of comparable size for each its radial cones. On the contrary, it is possible that radial cones of P admit much smaller extended formulations than P itself. A prominent example of this type is the perfectmatching polytope, which cannot be described by subexponentialsize extended formulations (Rothvoß 2014). However, Ventura & Eisenbrand (2003) showed that its radial cones can be described by polynomialsize extended formulations. Moreover, they generalized their construction to V join polyhedra. In the same paper, the authors asked whether the same holds for the oddcut polyhedron, the blocker of the V join polyhedron. We answer this question negatively. Precisely, we show that radial cones of oddcut polyhedra cannot be described by subexponentialsize extended formulations. To obtain our result, for a polyhedron P of blocking type, we establish a general relationship between its radial cones and certain faces of the blocker of P .
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