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CSI 3131
Assignment 4

Question 1
A page-replacement algorithm should minimize the number of page faults. We can
achieve this minimization by distributing heavily used
pages evenly over all of memory, rather than having them compete for a small number of
page frames. We can associate with each page frame
a counter of the number of pages associated with that frame. Then, to replace a page, we
can search for the page frame with the smallest
counter.
a. Define a page-replacement algorithm using this basic idea. Specifically address
these problems:
i. What the initial value of the counters is
ii. When counters are increased
iii. When counters are decreased
iv. How the page to be replaced is selected
b. How many page faults occur for your algorithm for the following reference string,
for four page frames?
1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2.
c. What is the minimum number of page faults for an optimal page replacement
strategy for the reference string in part b with four page frames?
Question 2
Write a program that implements the FIFO and LRU page-replacement algorithms
presented in this chapter. First, generate a random page-reference string where page
numbers range from 0 to 9. Apply the random page-reference string to each algorithm,
and record the number of page faults incurred by each algorithm. Implement the
replacement algorithms so that the number of page frames can vary from 1 to 7. Assume
that demand paging is used.
Question 3
The Catalan numbers are an integer sequence Cn that appear in tree-enumeration
problems. The first Catalan numbers for n=1,2,3,…. Are 1, 2, 5, 14, 42, 132, … A
formula generating Cn is:
Cn = (2n)!/(n+1)!n!
Design 2 programs (one for the producer and one for the consumer) that communicate
with shared memory on Windows or Unix/Linux. The producer process will generate
the Catalan sequence and write it to a shared memory object. The consumer process with
then read and output the sequence from shared memory. In this instance, the producer
process will be passed an integer parameter on the command line specifying the number
of Catalan numbers to produce; i.e., providing 5 on the command line means the producer
process will generate the first 5 Catalan numbers.