Exercise 7.2 Many computer applications involve searching through a set of data and sorting the data. A number of effi cient search ing and sorting algorithms have been devised in order to reduce the runtime of these tedious tasks. In this problem we will consider how best to parallelize these tasks.

7.2.1 [10] <7.2> Consider the following binary search algorithm (a classic divide and conquer algorithm) that searches for a value X in a sorted N-element array A and returns the index of the matched entry:
BinarySearch(A[0..N–1], X) {
low = 0 high = N – 1 while (low <= high) {
mid = (low + high) / 2 if (A[mid] > X)
high = mid – 1 else if (A[mid] < X)
low = mid + 1 else return mid // found }
return –1 // not found }
Assume that you have Y cores on a multicore processor to run BinarySearch.
Assuming that Y is much smaller than N, express the speed-up factor you might expect to obtain for values of Y and N. Plot these on a graph.
7.2.2 [5] <7.2> Next, assume that Y is equal to N. How would this affect your conclusions in your previous answer? If you were tasked with obtaining the best speed-up factor possible (i.e., strong scaling), explain how you might change this code to obtain it.