Permuting data on random-access block storage

Permutation is a fundamental operator for array data, with applications in, for example, changing matrix layouts and reorganizing data cubes. We consider the problem of permuting large quantities of data stored on secondary storage that supports fast random block accesses, such as solid state drives and distributed key-value stores. Faster random accesses open up interesting new opportunities for permutation. While external merge sort has often been used for permutation, it is an overkill that fails to exploit the property of permutation fully and carries unnecessary overhead in storing and comparing keys. We propose faster algorithms with lower memory requirements for a large, useful class of permutations. We also tackle practical challenges that traditional permutation algorithms have not dealt with, such as exploiting random block accesses more aggressively, considering the cost asymmetry between reads and writes, and handling arbitrary data dimension sizes (as opposed to perfect powers often assumed by previous work). As a result, our algorithms are faster and more broadly applicable.