Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
On the complexity of some basic problems in computational convexity: I.: containment problems
Discrete Mathematics - Special issue: trends in discrete mathematics
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
Handbook of computational geometry
Handbook of computational geometry
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
Construction of isothetic covers of a digital object: A combinatorial approach
Journal of Visual Communication and Image Representation
Reachability analysis of large-scale affine systems using low-dimensional polytopes
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Isothetic polygonal approximations of a 2d object on generalized grid
PReMI'05 Proceedings of the First international conference on Pattern Recognition and Machine Intelligence
TIPS: on finding a tight isothetic polygonal shape covering a 2d object
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Donut domains: efficient non-convex domains for abstract interpretation
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
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This paper deals with the problem of approximating a convex polytope in any finite dimension by a collection of (hyper)boxes. More exactly, given a polytope P by a system of linear inequalities, we look for two collections I and E of boxes with non-overlapping interiors such that the union of all boxes in I is contained in P and the union of all boxes in E contains P. We propose and test several techniques to construct I and E aimed at getting a good balance between two contrasting objectives: minimize the volume error and minimize the total number of generated boxes. We suggest how to modify the proposed techniques in order to approximate the projection of P onto a given subspace without computing the projection explicitly.