On Data Distributions in the Construction of Parallel Programs

Abstract

Data distributions have a serious impact on time complexity of parallel programs, developed based on domain decomposition. A new kind of distributions—set distributions, based on set-valued mappings, is introduced. These distributions assign a data object to more than one process. The set distributions can be used especially when the number of processes is greater than the data input size, but, sometimes using set distributions can lead to efficient general parallel algorithms. The work-load properties of these distributions and their impact on the number of communications are discussed. In order to illustrate the implications of data distributions in the construction of parallel programs, some examples are presented. Two parallel algorithms for computation of Lagrange interpolation polynomial are developed, starting from simple distributions and set distributions.