Massachusetts Institute of Technology
Handout 7
6.854J/18.415J: Advanced Algorithms
Wednesday, September 30, 2009
David Karger
Problem Set 4
Due: Wednesday, October 7, 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.
NONCOLLABORATIVE Problem 1.
The US Census Bureau produces a variety of
tables from its Census data. Suppose that it wishes to produce a
p
by
q
table
D
=
{
d
ij
}
of nonnegative integers. Let
r
i
denote the sum of the matrix elements in the
i
th
row, and
let
c
j
denote the sum of the elements in the
j
th
column. Assume that each sum
r
i
and
c
j
is
strictly positive. The Census Bureau often wishes to disclose all the row and column sums
along with some matrix elements (denoted by the set
Y
) and yet to suppress the remaining
elements to ensure the confidentiality of privileged information. Unless it exercises care, by
disclosing the elements in
Y
the Bureau might permit someone to deduce the exact value of
one or more suppressed elements. It is possible to deduce the exact value of an element
d
ij
if
only one value of
d
ij
is consistent with the row and column sums and the disclosed elements
in
Y
. We say that any such suppressed element is
unprotected
. Describe a polynomial time
algorithm for identifying all the unprotected elements of the matrix and their values.
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 Fall '09
 DavidKarger
 Algorithms, The Bible, Summation, United States Census Bureau, United States Census, minimum flow

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