Discrete & Computational Geometry

, Volume 41, Issue 2, pp 318–327 | Cite as

A Continuous d-Step Conjecture for Polytopes



The curvature of a polytope, defined as the largest possible total curvature of the associated central path, can be regarded as a continuous analogue of its diameter. We prove an analogue of the result of Klee and Walkup. Namely, we show that if the order of the curvature is less than the dimension d for all polytopes defined by 2d inequalities and for all d, then the order of the curvature is less that the number of inequalities for all polytopes.


Polytopes Diameter Hirsch conjecture d-Step conjecture Central path Curvature 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Advanced Optimization Laboratory, Department of Computing and Software, School of Computational Engineering and ScienceMcMaster UniversityHamiltonCanada

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