TY - GEN

T1 - On the exact maximum complexity of Minkowski sums of convex polyhedra

AU - Fogel, Efi

AU - Halperin, Dan

AU - Weibel, Christophe

PY - 2007

Y1 - 2007

N2 - We present a tight bound on the exact maximum complexity of Minkowski sums of convex polyhedra in R3. In particular, we prove that the maximum number of facets of the Minkowski sum of two convex polyhedra with m and n facets respectively is bounded from above by f(m, n) = 4mn-9m-9n+26. Given two positive integers m and n, we describe how to construct two convex polyhedra with m and n facets respectively, such that the number of facets of their Minkowski sum is exactly f(m, n). We generalize the construction to yield a lower bound on the maximum complexity of Minkowski sums of many convex polyhedra in R3. That is, given k positive integers m1,m2, . . .,mk, we describe how to construct k convex polyhedra with corresponding number of facets, such that the number of facets of their Minkowski sum is ∑ 1≤i

AB - We present a tight bound on the exact maximum complexity of Minkowski sums of convex polyhedra in R3. In particular, we prove that the maximum number of facets of the Minkowski sum of two convex polyhedra with m and n facets respectively is bounded from above by f(m, n) = 4mn-9m-9n+26. Given two positive integers m and n, we describe how to construct two convex polyhedra with m and n facets respectively, such that the number of facets of their Minkowski sum is exactly f(m, n). We generalize the construction to yield a lower bound on the maximum complexity of Minkowski sums of many convex polyhedra in R3. That is, given k positive integers m1,m2, . . .,mk, we describe how to construct k convex polyhedra with corresponding number of facets, such that the number of facets of their Minkowski sum is ∑ 1≤i

KW - Complexity

KW - Convex

KW - Minkowski sum

KW - Polyhedra

UR - http://www.scopus.com/inward/record.url?scp=35348861803&partnerID=8YFLogxK

U2 - 10.1145/1247069.1247126

DO - 10.1145/1247069.1247126

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AN - SCOPUS:35348861803

SN - 1595937056

SN - 9781595937056

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 319

EP - 326

BT - Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07

T2 - 23rd Annual Symposium on Computational Geometry, SCG'07

Y2 - 6 June 2007 through 8 June 2007

ER -