Massachusetts Institute of Technology
Handout 19
6.854J/18.415J: Advanced Algorithms
Friday, November 13, 2009
David Karger
Problem Set 10
Due: Wednesday, November 18, 2009.
Collaboration policy:
collaboration is
strongly encouraged
. However, remember that
1. You must write up your own solutions, independently.
2. You must record the name of every collaborator.
3. You must actually participate in solving all the problems. This is difficult in very large
groups, so you should keep your collaboration groups limited to 3 or 4 people in a given
week.
4.
No bibles. This includes solutions posted to problems in previous years.
Problem 1.
A problem last week found lines (and polygons)
contained
in a rectangle; here
we consider finding lines
crossing
a rectangle. As a starting point, suppose you are given an
interval tree
data structure. This takes
n
possiblyoverlapping intervals on the real line, and
builds a size
n
data structure that can, in
O
(
k
+ log
n
) time, output the set of all intervals
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 Fall '09
 DavidKarger
 Algorithms, Decision tree model, Model of Computation, Voronoi diagram

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