Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Balanced partitions of two sets of points in the plane
Computational Geometry: Theory and Applications
Radial Perfect Partitions of Convex Sets in the Plane
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Finding equitable convex partitions of points in a polygon efficiently
ACM Transactions on Algorithms (TALG)
| Hi-index | 0.00 |
We consider the following problem. Let n 驴 2, b 驴 1 and q 驴 2 be integers. Let R and B be two disjoint sets of nred points and bn blue points in the plane, respectively such that no three points of R驴B lie on the same line. Let n = n1 + n2 + ... + nq be an integer-partition of n such that 1 驴 ni for every 1 驴 i 驴 q. Then we want to partition R驴B into qdisjoint subsets P1 驴 P2 驴 ... 驴 Pqthat satisfy the following two conditions: (i)conv (Pi)驴 conv (Pj)= 驴 for all 1 驴 i j 驴 q, where conv(Pi) denotes the convex hull of Pi; and (ii) each Pi contains exactly ni red points and bni blue points for every 1 驴 i 驴 q.We shall prove that the above partition exits in the case where (i) 2 驴 n 驴 8 and 1 驴 ni 驴 n/2 for every 1 驴 i 驴 qand (ii) n1 = n2 = ... = nq-1 = 2 and nq=1.