Optimisation of digraphs creation for parallel algorithm for finding a complete set of solutions of characteristic polynomial

• Published in: 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR) pp. 1139 - 1144
• Main Authors: Hryniow, Krzysztof, Markowski, Konrad Andrzej
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.08.2015
• Subjects: characteristic polynomial; Computational complexity; digraph; GPGPU; Graphics processing units; Kernel; Mathematical model; optimisation; Parallel algorithms; parallel computation; Polynomials
• DOI: 10.1109/MMAR.2015.7284039

This paper presents a series of further modifications to the parallel algorithm used for finding digraphs realisations of the characteristic polynomial. What distinguishes the mentioned algorithm from other state-of-the-art solutions is the ability to find a complete set of existing solutions, not just a few of them. Moreover, solutions found tend to be minimal in terms of a rank of matrices created. Due to a of large number of solutions tested and an NP-hard complexity of the problem, the parallel algorithm is incapable of finding solutions for more complicated problems in reasonable time. To address this problem additional modifications of the algorithm structure are proposed and explained. Modifications presented in this paper contribute to a reduction of a number of improper solutions that are created, and later tested and rejected, by the algorithm making it work in all cases, except the most trivial ones, at least by an order of magnitude faster.