Develop a Parallel Algorithm for addition of Two Sparse Matrices. Make necessary assumptions.
### Parallel Algorithm for Addition of Two Sparse Matrices
Sparse matrices are matrices in which most of the elements are zero. The addition of two sparse matrices is a common operation in numerical computing, and it can benefit significantly from parallelization due to the sparse nature of the matrices. A parallel algorithm for adding sparse matrices ensures that the operation is carried out efficiently by utilizing multiple processors simultaneously, reducing the overall computational time. In this section, we will develop a parallel algorithm for the addition of two sparse matrices, making necessary assumptions along the way.
### Assumptions
To develop an efficient parallel algorithm for the addition of two sparse matrices, we make the following assumptions:
1. Matrix Representation: We will use the Compressed Sparse Row (CSR) format to represent sparse matrices. This format stores non-zero elements along with their row and column indices, which is space-efficient and allows faster access to the non-zero elements.
- In CSR format, a matrix is represented by three arrays:
- `values[]`: stores the non-zero values of the matrix.
- `column_indices[]`: stores the column indices corresponding to the non-zero values.
- `row_pointer[]`: stores the index in `values[]` where each row starts, with an additional entry for the end of the last row.
2. Matrix Size: We assume the matrices are of size `m x n` ____ ____ _____ ______ ________.
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