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2D partitioning: Every processor gets a submatrix of the adjacency matrix. Assume the processors are aligned in a rectangle <math>p = p_r \times p_c</math>, where <math>p_r
2D partitioning: Every processor gets a submatrix of the adjacency matrix. Assume the processors are aligned in a rectangle <math>p = p_r \times p_c</math>, where <math>p_r
2 d 分区: 每个处理器都有一个邻接矩阵的子矩阵。假设处理器在一个矩形 <math> p = p_r 乘以 p_c </math> 中对齐，其中 <math> p_r
2 d 分区: 每个处理器都有一个邻接矩阵的子矩阵。假设处理器在一个矩形 <math>p = p_r 乘以 p_c</math> 中对齐，其中 <math>p_r</math>and<math>p_c</math>and<math>p_c[/math ]和[ math ]</math> are the amount of processing elements in each row and column, respectively. Then each processor gets a [[submatrix]] of the adjacency matrix of dimension <math>(n/p_r)\times(n/p_c)</math>. This can be visualized as a [[checkerboard]] pattern in a matrix.<ref name=":2" /> Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to <math>p_r + p_c - 1</math> out of <math>p = p_r \times p_c</math> possible ones.
</math>and<math>p_c
</math>and<math>p_c
[/math ]和[ math ]
</math> are the amount of processing elements in each row and column, respectively. Then each processor gets a [[submatrix]] of the adjacency matrix of dimension <math>(n/p_r)\times(n/p_c)</math>. This can be visualized as a [[checkerboard]] pattern in a matrix.<ref name=":2" /> Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to <math>p_r + p_c - 1</math> out of <math>p = p_r \times p_c</math> possible ones.
</math> are the amount of processing elements in each row and column, respectively. Then each processor gets a submatrix of the adjacency matrix of dimension <math>(n/p_r)\times(n/p_c)</math>. This can be visualized as a checkerboard pattern in a matrix. Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to <math>p_r + p_c - 1</math> out of <math>p = p_r \times p_c</math> possible ones.
</math> are the amount of processing elements in each row and column, respectively. Then each processor gets a submatrix of the adjacency matrix of dimension <math>(n/p_r)\times(n/p_c)</math>. This can be visualized as a checkerboard pattern in a matrix. Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to <math>p_r + p_c - 1</math> out of <math>p = p_r \times p_c</math> possible ones.