TY - GEN

T1 - On Neighbors in Geometric Permutations

AU - Sharir, Micha

AU - Smorodinsky, Shakhar

N1 - Funding Information:
Work on this paper has been supported by NSF Grants CCR-97-32101 and CCR-00-98246, by a grant from the US–Israeli Binational Science Foundation, by a grant from the Israeli Academy of Sciences for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski—MINERVA Center for Geometry at Tel Aviv University.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - We introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the maximum number of neighbors in a set S of n pairwise disjoint convex bodies in ℝd is O(n), and we prove this conjecture for d = 2. We show that if the set of pairs of neighbors in a set S is of size N, then S admits at most O(Nd−1) geometric permutations. Hence we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any finite family of pairwise disjoint convex bodies in the plane.

AB - We introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the maximum number of neighbors in a set S of n pairwise disjoint convex bodies in ℝd is O(n), and we prove this conjecture for d = 2. We show that if the set of pairs of neighbors in a set S is of size N, then S admits at most O(Nd−1) geometric permutations. Hence we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any finite family of pairwise disjoint convex bodies in the plane.

UR - http://www.scopus.com/inward/record.url?scp=84943239043&partnerID=8YFLogxK

U2 - 10.1007/3-540-45471-3_14

DO - 10.1007/3-540-45471-3_14

M3 - Conference contribution

AN - SCOPUS:84943239043

SN - 9783540438663

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 131

EP - 139

BT - Algorithm Theory, SWAT 2002

A2 - Penttonen, Martti

A2 - Schmidt, Erik Meineche

PB - Springer Verlag

T2 - 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002

Y2 - 3 July 2002 through 5 July 2002

ER -