1 Union d`ellipses 2 Arrangement de droites

n
n n
s s
n

S2n n x y = 0 n
y > 0
S
droites non ordinaires
droite ordinaire
p S p
p S yp>0
p
En

E
E
n
n n
s
s
n

Θ(nα(n))
O(nα(n) log n)
Θ(nlog n)
•n
x= 0
•n x1< x2< . . . < x2n
[x1, x2n] [xi, xj] [xi, xk] [xk, xj]k=b(i+j)/2c
[xi, xi+1]
n
O(log n)
O(log n)
n n
IR
n i t
pi(t) = qi+tvi, qi, vi∈IR2
pi(t) = qi+tvi+t2g g

a
b
c
a
b
c
abca acbcacbca
O(n2α(n))
acdbdcbcdbdca
a
b
c
d
a
b
c
d
acdbdbdcacdca
acdbdcbcdbdca acdbdbdcacdca
O(n2α(n)log n)
n n(n−1)/2
n
n x n y