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CS 373U
Homework 6 (Practice only)
Spring 2004
1. Let
P
be a set of
n
points in the plane. Recall that a point
p
∈
P
is
Paretooptimal
if no other
point is both above and to the right of
p
. Intuitively, the sorted sequence of Paretooptimal
points describes a
staircase
with all the points in
P
below and to the left. Your task is to
describe some algorithms that compute this staircase.
The staircase of a set of points
(a) Describe an algorithm to compute the staircase of
P
in
O
(
nh
) time, where
h
is the
number of Paretooptimal points.
(b) Describe a divideandconquer algorithm to compute the staircase of
P
in
O
(
n
log
n
)
time.
[Hint: I know of at least two diFerent ways to do this.]
⋆
(c) Describe an algorithm to compute the staircase of
P
in
O
(
n
log
h
) time, where
h
is the
number of Paretooptimal points.
[Hint: I know of at least two diFerent ways to do this.]
(d) Finally, suppose the points in
P
are already given in sorted order from left to right.
Describe an algorithm to compute the staircase of
P
in
O
(
n
) time.
[Hint: I know of at
least two diFerent ways to do this.]
2. Let
R
be a set of
n
rectangles in the plane.
(a) Describe and analyze a plane sweep algorithm to decide, in
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 Fall '08
 Chekuri,C
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