CS 140
Midterm 2

3 March 2010
Name
Perm#
Problem 1 [20 points total]
This problem is about maximal
independent sets in the graph shown at right, which has 12 vertices
connected in a cycle with 12 edges.
For each part, you are to first
identify a particular maximal independent set (or MIS), and then label
the vertices to show how one of the algorithms we studied in class
could find that particular MIS.
(1a) [5 points]
On the copy of the graph below, identify a
largest possible
maximal independent set
by coloring in the vertices of that set.
(1b) [5 points]
On the same graph below, label the vertices with the integers 1, 2, …, 12 in such a
way that the
sequential
MIS
algorithm
would find the same MIS you’ve colored in.
(1c) [5 points]
On the copy of the graph below, identify a
smallest possible
maximal independent
set by coloring in the vertices of that set.
(1d) [5 points]
On the same graph below, label the vertices with 2digit numbers (like 3.1, 2.7, 1.9)
in such a way that, if the
randomized parallel MIS algorithm
happened to choose those random
numbers, it would take just one round to find the same MIS you’ve colored in.
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Perm#
Problem 2 [20 points total]
Recall that we have two ways to measure communication cost:
(1)
Communication
volume
v
counts the total number of data words that move from any processor
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 Fall '11
 GILBERT
 Prime number, 2digit, Jacobi iteration, maximal independent set, cilk++

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