Cuboids-Shearsort-MPI

An implementation of the Shearsort algorithm for parallel sorting an array. This implementation is using another parallel sorting algorithm which is Odd-Even sort.

In this implementation, a bench of cuboids is read from an input file into an array, which contain each cuboid's id, width, height, and depth. The cuboids are being sorted by the volume of each, or by the width if the volume is equals.

Each process gets a cuboid by MPI_Scatter and returns its value in the end of the algorithm with MPI_Gather.

Shearsort Iterations

This algorithm sorting an array of nXn values with nXn processes after iterations, each iteration is complexity, (in this case ) so the final complexity time is .

Initial

The processes are cartesian ordered by MPI_Cart_create.

| 14 |  1 | 13 |  8 |  
|  4 | 11 |  6 |  7 |  
| 12 |  9 | 10 |  5 |  
|  3 |  2 |  0 | 15 |

Even Iterations

In even iteration, each row of the matrix is sorted in ascending order if it is an even row, or in descending order if it is an odd row.

|  1 |  8 | 13 | 14 |    ->
| 11 |  7 |  6 |  4 |    <-
|  5 |  9 | 10 | 12 |    ->
| 15 |  3 |  2 |  0 |    <-

Odd Iterations

In odd iteration, each column of the matrix is sorted in ascending order regardless if it is an even or odd column.

   ^    ^    ^    ^
|  1 |  3 |  2 |  0 |
|  5 |  7 |  6 |  4 |
| 11 |  8 | 10 | 12 |
| 15 |  9 | 13 | 14 |

End of Iterations

At the end of the iterations, the matrix will be as below.

|  0 |  1 |  2 |  3 |
|  7 |  6 |  5 |  4 |
|  8 |  9 | 10 | 11 |
| 15 | 14 | 13 | 12 |

All that left is to collect the values by a snake shape.

|  0 |  1 |  2 |  3 |   >
|  7 |  6 |  5 |  4 |   <
|  8 |  9 | 10 | 11 |   > 
| 15 | 14 | 13 | 12 |   <

Odd-Even Sort Iterations

This algorithm sorting an array of n values with n processes after n iterations. Complexity time .

Initial

The initial array will be as below.

Rank:   |  0 |  1 |  2 |  3 |

Value:  |  3 |  2 |  0 |  1 |     <-  the actual array

Even Iterations

In even iterations, an even-ranked process is communicating with his right odd-ranked neighbor. In ascending order, the even-ranked process will save the smaller value, while the odd-ranked process will save the greater one.

    >-<       >-<
|  3 |  2 |  0 |  1 |

So after the iteration, the array will look like below:

|  2 |  3 |  0 |  1 |

Odd Iterations

In odd iterations, an odd-ranked process will communicate with his right even-ranked process. The odd-ranked process will save the smaller value while the even-ranked process will save the greater one.

         >-<
|  2 |  3 |  0 |  1 |

So after the iteration, the array will look like below:

|  2 |  0 |  3 |  1 |

End of Iterations

At the end of the iterations, the array will be as below.

|  0 |  1 |  2 |  3 |