Data cube construction is a commonly used operation in data warehouses. Because of the volume of data that is stored and analyzed in a data warehouse and the amount of computation involved in data cube construction, it is natural to consider parallel machines for this operation. This paper addresses a number of algorithmic issues in parallel data cube construction. First, we present an aggregation tree for sequential (and parallel) data cube construction, which has minimally bounded memory requirements. An aggregation tree is parameterized by the ordering of dimensions. We present a parallel algorithm based upon the aggregation tree. We analyze the interprocessor communication volume and construct a closed form expression for it. We prove that the same ordering of the dimensions minimizes both the computational and communication requirements. We also describe a method for partitioning the initial array and prove that it minimizes the communication volume. Experimental results from implementation of our algorithms on a cluster of workstations validate our theoretical results.