TY - GEN
T1 - On neighbors in geometric permutations
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
PY - 2002/1/1
Y1 - 2002/1/1
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 - 8th Scandinavian Workshop on Algorithm Theory, Proceedings
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 -