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CS531
Final Exam
Winter, 1998
This exam is closed book
.
Answer all questions in the blue books.
Unsupported work
will receive no credit.
1.
(10%) Prove that
1
1
k
n
k
n
=
∑
= Θ
(log ).
2.
(10%) Draw an 8element
bitonic sort
unit.
3.
Given a set of
n
integer
values in the range of [1,100], for each of the following
architectures, give an efficient algorithm to sort these data items.
Discuss the
quality of each of your solutions in terms of time/space/processors.
a)
(10%) RAM
b)
(10%) PRAM
4.
Define a
Reconfigurable Array of size n
to be a linear array augmented by a
reconfigurable bus
.
The reconfigurable bus has the characteristic that every
processor has the ability to split or connect the bus between itself and either (or
both or neither) of its neighbors during
every step of an algorithm
.
That is, the
bus can be dynamically reconfigured on the fly.
Further, on each bus segment,
only 1 processor can perform a write and all processors can read the value written
(i.e., the bus is CREW within each independent segment).
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 Spring '09
 Algorithms

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