Geodesic
The Linear Inequalities Set Representation of Minkovski's Sum for Two Polyhedrons
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 108-119

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A convex polyhedron is represented as a set of the linear inequalities solutions. Minkowski's sum of two convex polyhedrons $X,Y\subset \mathbb{R}^n$ is polyhedron as well is represented as a set of the linear inequalities solutions. Polynomial algorithm of solving this problem based of forming number of extra inequalities in the summands representation and them translation to resultant representation is presented in the paper. Usage of parallel and distributed computation for effective algorithm Implementation is suggested.
Keywords: polyhedron, Minkowski's sum set, linear inequalities set, linear programming. 
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     author = {A. V. Panyukov},
     title = {The {Linear} {Inequalities} {Set} {Representation} of  {Minkovski's} {Sum} for  {Two} {Polyhedrons}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {108--119},
     publisher = {mathdoc},
     number = {14},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_14_a10/}
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A. V. Panyukov. The Linear Inequalities Set Representation of  Minkovski's Sum for  Two Polyhedrons. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 108-119. http://geodesic.mathdoc.fr/item/VYURU_2012_14_a10/