2019/08/15 by Ji Hoon Chun, Chun, Ji Hoon
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Optimization and Packing Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1908.05650
The problem of finding the largest number of points in the unit cross-polytope such that the l1-distance between any two distinct points is at least 2r is investigated for r∈(1-(1)/(n),1] in dimensions ≥2 and for r∈((1)/(2),1] in dimension 3. For the n-dimensional cross-polytope, 2n points can be placed when r∈(1-(1)/(n),1]. For the three-dimensional cross-polytope, 10 and 12 points can be placed if and only if r∈((3)/(5),(2)/(3)] and r∈((4)/(7),(3)/(5)] respectively, and no more than 14 points can be placed when r∈((1)/(2),(4)/(7)]. Also, constructive arrangements of points that attain the upper bounds of 2n, 10, and 12 are provided, as well as 13 points for dimension 3 when r∈((1)/(2),(6)/(11)].