TY - JOUR
T1 - On the exact maximum complexity of Minkowski sums of polytopes
AU - Fogel, Efi
AU - Halperin, Dan
AU - Weibel, Christophe
N1 - Funding Information:
This work has been supported in part by the IST Programme of the EU as Shared-cost RTD (FET Open) Project under Contract No IST-006413 (ACS—Algorithms for Complex Shapes), by the Israel Science Foundation (grant no. 236/06), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.
PY - 2009/10
Y1 - 2009/10
N2 - We present a tight bound On the exact maximum complexity of Minkowski sums of polytopes in ℝ3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2,...,mk facets, respectively, is bounded from above by. Given k positive integers m1,m2,...,mk, we describe how to construct k polytopes with corresponding number of facets, such that the number of facets of their Minkowski sum is exactly. When k=2, for example, the expression above reduces to 4m1m2-9m1-9m2+26.
AB - We present a tight bound On the exact maximum complexity of Minkowski sums of polytopes in ℝ3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2,...,mk facets, respectively, is bounded from above by. Given k positive integers m1,m2,...,mk, we describe how to construct k polytopes with corresponding number of facets, such that the number of facets of their Minkowski sum is exactly. When k=2, for example, the expression above reduces to 4m1m2-9m1-9m2+26.
KW - Complexity
KW - Gaussian maps
KW - Minkowski sum
KW - Polyhedra
UR - http://www.scopus.com/inward/record.url?scp=70350704848&partnerID=8YFLogxK
U2 - 10.1007/s00454-009-9159-1
DO - 10.1007/s00454-009-9159-1
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AN - SCOPUS:70350704848
SN - 0179-5376
VL - 42
SP - 654
EP - 669
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 4
ER -