Parallel algorithms for the solution of large sparse inequality systems on distributed memory architectures

Abstract

In this thesis, several parallel algorithms are proposed and utilized for the solution of large sparse linear inequality systems. The parallelization schemes are developed from the coarse-grain parallel formulation of the surrogate constraint method, based on the partitioning strategy: 1D partitioning and 2D partitioning. Furthermore, a third parallelization scheme is developed for the explicit minimization of the communication overhead in 1D partitioning, by using hypergraph partitioning. Utilizing the hypergraph model, the communication overhead is maintained via a global communication scheme and a local communication scheme. In addition, new algorithms that use the bin packing heuristic are investigated for efficient load balancing in uniform rowwise stripped and checkerboard partitioning. A general class of image recovery problems is formulated as a linear inequality system. The restoration of images blurred by so called point spread functions arising from effects such as misfocus of the photographic device, atmospheric turbulence, etc. is successfully provided with the developed parallel algorithms.