Ownership sets are fundamental to the partitioning of program computations across processors by the owner-computes rule. These sets arise due to the mapping of data arrays onto processors. In this paper, ^a we focus on how ownership sets can be efficiently determined in the context of the HPF language, and show how the structure of these sets can be symbolically characterized in the presence of arbitrary data alignment and data distribution directives. Our starting point is a system of equalities and inequalities due to Ancourt et al. that captures the array mapping problem in HPF. We arrive at a refined system that enables us to efficiently solve for the ownership set using the Fourier-Motzkin Elimination technique, and which requires the course vector as the only auxiliary vector. We develop ^b important and general properties pertaining to HPF alignments and distributions, and show how they can be used to eliminate redundant communication due to array replication. We also show how the generation of communication code can be avoided when pairs of array references are ultimately mapped onto the same processors. Experimental data demonstrating the improved code performance that the latter optimization enables is presented and discussed.