Parallel Algorithms: Theory and Practice CS260 –
Author : danika-pritchard | Published Date : 2025-05-12
Description: Parallel Algorithms Theory and Practice CS260 Lecture 3 Yihan Sun Some of the slides are from MIT 6712 6886 and CMU 15853 Last Lecture Two scan algorithms Divideandconquer Reduce the problem size Computational models PRAM
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Transcript:Parallel Algorithms: Theory and Practice CS260 –:
Parallel Algorithms: Theory and Practice CS260 – Lecture 3 Yihan Sun * Some of the slides are from MIT 6.712, 6.886 and CMU 15-853. Last Lecture Two scan algorithms Divide-and-conquer Reduce the problem size Computational models PRAM Fork-join: N-way vs. binary Atomic primitives Implement parallel algorithms using C++ I’ll ask for your feedback (about) every two lectures, you can be prepared for that 2 In this lecture Matrix multiplication Solve recurrences using Master Theorem Some applications that can be solved in parallel 3 Homework 1 The deadline has been extended to 27th Jan – 5 more days Code submitted to iLearn If you want to use the late days, let me know After this lecture, you’ll be able to solve all the problems in Homework 1 4 Course Website: https://www.cs.ucr.edu/~yihans/teaching/palgo.html Under my UCR homepage Matrix Multiplication 5 Matrix Multiplication Consider standard iterative matrix-multiplication algorithm X Y Z := for i = 1 to N do for j = 1 to N do for k = 1 to N do Z[i][j] += X[i][k] * Y[k][j] Matrix Multiplication 7 for i = 1 to N do for j = 1 to N do for k = 1 to N do Z[i][j] += X[i][k] * Y[k][j] par_for i = 1 to N do par_for j = 1 to N do for k = 1 to N do Z[i][j] += X[i][k] * Y[k][j] par_for i = 1 to N do par_for j = 1 to N do par_for k = 1 to N do temp[k] = X[i][k] * Y[k][j]; Z[i][j] = parallel_reduce(temp, N); Recursive Matrix Multiplication X11 Y11 Z11 := Z12 Z21 Z22 X12 X21 X22 Y21 Y12 Y22 Compute 8 submatrix products recursively Z11 := X11Y11 + X12Y21 Z12 := X11Y12 + X12Y22 Z21 := X21Y11 + X22Y21 Z22 := X21Y12 + X22Y21 Matrix Multiplication 9 How to solve a recurrence in general? 10 Solving recurrences – Master Theorem 11 12 … … … … 13 … … 14 … … 15 … 16 … … … You can always analyze a specific algorithm using the tree … Master Theorem 17 Matrix multiplication 18 Master Theorem Quiz 19 Use recurrence to compute work and depth 20 S1; S2; In parallel: S1; S2; Case 1: S = execute S2 after finishing S1 Case 2: S = execute S2 and S1 in parallel Flatten algorithm 21 Flatten Algorithm 22 Flatten algorithm 23 Flatten(A, n) {
