Efficient placement of parity and data to tolerate two disk failures in disk array systems

In this paper, we deal with the data/parity placement problem which is described as follows: how to place data and parity evenly across disks in order to tolerate two disk failures, given the number of disks N and the redundancy rate p which represents the amount of disk spaces to store parity information. To begin with, we transform the data/parity placement problem into the problem of constructing an N×N matrix such that the matrix will correspond to a solution to the problem. The method to construct a matrix has been proposed and we have shown how our method works through several illustrative examples. It is also shown that any matrix constructed by our proposed method can be mapped into a solution to the placement problem if a certain condition holds between N and p where N is the number of disks and p is a redundancy rate