# 20 Years of Teaching Parallel Processing to Computer Science Seniors

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4 Figure 2. CPU utilization on parallel matrix multiplication -- all cores are at 100% for several minutes With Microsoft's Visual Studio, we can easily fire up many cores using the "parallel for" structure. Once a program, such as matrix-multiplication, starts as shown in Figure 2, CPU utilization can quickly reach 100%, and having 99% of overall CPU time is dedicated to the problem. The figure shows that every core has been running at 100% for some times already. For many students, this is the first time they have seen any computer working this hard. At this point, most students are very eager to try their hands on coding some parallel algorithms and start to think about all kinds of problems that could benefit from this newly mastered skill. C. Inspect a known problem from a different angle In parallel programming classes, we often discuss developing parallel algorithms for a well-known problem. However, if we look a problem from a different angle, we may reach different solutions, possibly parallel solutions. For example, merging two sorted array of size n is a classical data structure problem with a complexity of O(n). On PRAM with n processors, we can solve the problem in O(log n) as showing in Figure 3. MergeArray(A[1..n]) { int x, i, low, high, index for all where 1 <= i <= n // The lower half search the upper half, // the upper half search for the lower half { high = 1 // assuming it is the upper half low = n/2 if i <= (n/2) { high = n low = (n/2) + 1 x = A[i] Repeat // perform binary search { index = floor((low + high)/2) If x < A[index] high = index 1 else low = index + 1 until low > high A[high + i n/2] = x Figure 3. Merging an array of n elements with two sorted halves in parallel on PRAM Assuming two sorted arrays are stored in the two halves of a larger array, the outline of the algorithm is as follow. For a given element a i in the first half of the array, we can find out the number of elements in the second half that are smaller than it (denoted as POS) by using binary search in O(log n) time as if we were to insert a i into the second half. We know there are i elements that are smaller than a i in the first half, so there are total of i + POS elements that are smaller than a i in the entire collection. We can then just copy a i into in the final merged array's slot at i + POS. Using n processors to merge the two half arrays (of n/2 elements each) takes O(log n) time because each processor works independently and concurrently. Figure 4 attempts to illustrate the algorithm with a real example. In Figure 4, let's assume the top array is the first half of the array needs to be merged. Let's use A[1] (zero based), which has a value of 4, as an example. Since its index is 1, it has 1 element smaller than it in its half of the array. If we were to insert A[1] into the second half, it would have taken the slot of the fourth element, that is POS = 3. That is, there are three elements smaller than A[1] in the second half of the array. This can be determined in O(log n) time using the binary search algorithm. So in total, there are four elements smaller than A[1]. Therefore, we can just copy A[1] into the fifth element of the final array, as showing in Figure Figure 4. Merging an array with two sorted halves. This algorithm generates a lot of interests among students because the parallel solution is relatively speaking easy to understand. In addition, students already know the problem well and understand the sequential algorithms used in the parallel solution well too. However, the key in the parallel solution is to look into the problem differently. Instead of finding an element to be copied into a given slot of the final array (as we do in our sequential solution), the new algorithm take the opposite approach. For a given array element, the algorithm finds the slot where the final element should be stored and copy the element

7 believe that teaching PDC concepts to Computer Science undergraduates is both necessary and can be extremely beneficial to students future growth. We have shared several of our approaches that make the class much more interesting to hope that more and more students can enjoy taking such a class. We also have presented much details of our Concurrent Systems class, where many PDC concepts are taught for more than 20 years. With the right approaches, we managed to find resources to support several rounds of changes in hardware. We believe the class allows students to learn parallel computer organizations, study parallel algorithms, and write code to be able to run on parallel and distributed platforms. We also shared our plan for attracting more students to become interested in learning PDC concepts and parallel programming. ACKNOWLEDGMENT We would like to thank the WOU s Faculty Development Committee, NSF, and the division of Computer Science at WOU for supporting our efforts. We also would like to let our anonymous reviewers to know that we deeply appreciate their comments, corrections, and suggestions. REFERENCES [1] Quinn, Michael J. Parallel Computing: Theory and Practice. 2d ed. New York: McGraw-Hill, 1994 [2] Liu J. and F. Liu, Teaching Parallel Programming with Multi-core Computers, The 2010 Intl. Conf. on Frontiers in Education: Computer Science and Computer Engineering, July 12-15, 2010 [3] Brookshear, Glenn J. Computer Science and overview, 10ed Addison- Wesley, [4] [5] [6] [7] Hurtgen, Alyssa. High Performance Computing Cluster in a Cloud Environment, June, 2016 [8] Barney, Blaise. Introduction to Parallel Computing [9] Morgan, Timothy. Intel Knights Landing Yields Big Bang For The Buck Jump, June 20, 2016

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