The representation choice was actually where I spent most of my time.
Start by choosing a sparse representation like CSR or CSC that suits the multiplication order, then describe an algorithm that iterates only over non-zero elements, such as the row-wise SMMP algorithm. Finally, analyze complexity in terms of non-zero counts (nnz) and discuss trade-offs like memory vs. speed and potential parallelization.
Pro tip: Mention that the output sparsity pattern is not known in advance, so using a dynamic structure like a hash map or a two-pass approach (symbolic then numeric) can avoid expensive reallocations. Also, highlight that for ML workloads, leveraging optimized libraries (e.g., cuSPARSE) is often preferred over custom implementations unless specific constraints apply.
Select a representation like CSR, CSC, or COO based on the multiplication order and access patterns. Justify your choice in terms of efficiency for row-wise or column-wise operations.
Describe an algorithm that iterates only over non-zero elements, such as for each non-zero A[i,k], iterate over non-zeros in row k of B and accumulate into row i of C. Avoid dense loops over zeros.
Explain how to accumulate results efficiently, e.g., using a dense accumulator array for each row of C, then compress to sparse format. Discuss trade-offs of using a hash map for dynamic sparsity.
Express time complexity in terms of nnz(A), nnz(B), and nnz(C), e.g., O(nnz(A) * avg non-zeros per row of B). Discuss space complexity and compare with dense multiplication.
Mention potential optimizations like blocking, parallelization, or using specialized libraries. Discuss trade-offs between memory usage, speed, and implementation complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.