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 -