OpenMP-based Parallel Algorithms for Solving Kronecker Descriptors

Numerical analysis of Markovian models is relevant for performance evaluation and probabilistic analysis of systems´ behavior from several fields such as Bioinformatics, Economics, and Engineering. These models can be represented in a compact fashion using Kronecker algebra. The Vector-Descriptor Product is the key operation to obtain stationary solutions of Kronecker-based descriptors. Due to its complexity, the numerical algorithms are usually CPU intensive, requiring alternatives such as data partitioning in order to produce results in less time. This paper proposes three OpenMP-based parallel implementations for solving descriptors to be deployed on shared-memory machines. We evaluated the implementations in a multi-core machine and obtained a speed-up near to eight when using eight cores with Intel Hyper-Threading technology.