The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Supposons que 2m points rouges et 2n des points bleus sont indiqués sur le réseau Z2 dans l'avion R2. Nous montrons que s’ils sont en position générale, c’est-à-dire si au plus un point se trouve sur chaque ligne verticale et ligne horizontale, alors il existe une coupe rectangulaire qui coupe en deux les points rouges et les points bleus. De plus, s'ils ne sont pas en position générale, c'est-à-dire si certaines lignes verticales et horizontales peuvent contenir plus d'un point, alors il existe une coupe semi-rectangulaire qui coupe en deux les points rouges et les points bleus. Nous montrons également que ces résultats sont les meilleurs possibles dans un certain sens. De plus, notre preuve donne O(N enregistrer N), N=2m+2n, algorithme temporel pour trouver la coupe souhaitée.
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copier
Miyuki UNO, Tomoharu KAWANO, Mikio KANO, "Bisections of Two Sets of Points in the Plane Lattice" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 2, pp. 502-507, February 2009, doi: 10.1587/transfun.E92.A.502.
Abstract: Assume that 2m red points and 2n blue points are given on the lattice Z2 in the plane R2. We show that if they are in general position, that is, if at most one point lies on each vertical line and horizontal line, then there exists a rectangular cut that bisects both red points and blue points. Moreover, if they are not in general position, namely if some vertical and horizontal lines may contain more than one point, then there exists a semi-rectangular cut that bisects both red points and blue points. We also show that these results are best possible in some sense. Moreover, our proof gives O(N log N), N=2m+2n, time algorithm for finding the desired cut.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.502/_p
Copier
@ARTICLE{e92-a_2_502,
author={Miyuki UNO, Tomoharu KAWANO, Mikio KANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bisections of Two Sets of Points in the Plane Lattice},
year={2009},
volume={E92-A},
number={2},
pages={502-507},
abstract={Assume that 2m red points and 2n blue points are given on the lattice Z2 in the plane R2. We show that if they are in general position, that is, if at most one point lies on each vertical line and horizontal line, then there exists a rectangular cut that bisects both red points and blue points. Moreover, if they are not in general position, namely if some vertical and horizontal lines may contain more than one point, then there exists a semi-rectangular cut that bisects both red points and blue points. We also show that these results are best possible in some sense. Moreover, our proof gives O(N log N), N=2m+2n, time algorithm for finding the desired cut.},
keywords={},
doi={10.1587/transfun.E92.A.502},
ISSN={1745-1337},
month={February},}
Copier
TY - JOUR
TI - Bisections of Two Sets of Points in the Plane Lattice
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 502
EP - 507
AU - Miyuki UNO
AU - Tomoharu KAWANO
AU - Mikio KANO
PY - 2009
DO - 10.1587/transfun.E92.A.502
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2009
AB - Assume that 2m red points and 2n blue points are given on the lattice Z2 in the plane R2. We show that if they are in general position, that is, if at most one point lies on each vertical line and horizontal line, then there exists a rectangular cut that bisects both red points and blue points. Moreover, if they are not in general position, namely if some vertical and horizontal lines may contain more than one point, then there exists a semi-rectangular cut that bisects both red points and blue points. We also show that these results are best possible in some sense. Moreover, our proof gives O(N log N), N=2m+2n, time algorithm for finding the desired cut.
ER -