Grigni : [ 9 ] On the Complexity of the Generalized Block Distribution

We consider the problem of mapping an array onto a mesh of processors in such a way that locality is preserved. When the computational work associated with the array is distributed in an unstructured way the generalized block distribution has been recognized as an e cient way of achieving an even load balance while at the same time imposing a simple communication pattern. In this paper we consider the problem of computing an optimal generalized block distribution. We show that this problem is NP-complete even for very simple cost functions. We also classify a number of variants of the general problem.