CS 4540, Advanced Algorithms
Homework 1
Mon, Aug 30, 2010
Due Fri, Sept 10, 2010
Problem 1
Exercise 3, pages 782(bottom)784(top) of Chapter 13 ”Randomized Algorithms” by Kleinberg and
Tardos (posted in class lecture notes and assinged reading 082310). Recommendation:
In addition
to lecture notes and assigned reading of 082310, it will be quite useful to go over Solved Exercise
1, pages 776(bottom)779(top) of Chapter 13 ”Randomized Algorithms” by Kleinberg and Tardos.
Problem 2
Suppose that
n
distributed noncommunicating processes want to access a machine
M
where, if
more than two processes attempt to access
M
at the same time unit, then
M
rejects all requests,
but if at most two processes attempt to acess
M
at the same time unit, then
M
satisﬁes their
requets. (a) Suppose that, at each time unit, each process attempts to access
M
with probability
1
n
. Determine a value
t
as a function of
n
and
c
such that, the probability that all processes
n
have
succeeded in accessing
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 Fall '10
 Staff
 Algorithms, Probability theory, probability density function, time units

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