Optimisation of digraphs-based realisations for polynomials of one and two variables

Abstract

This paper proposes a set of modifications to the algorithm proposed earlier, that finds a complete set of minimal solutions for the characteristic polynomial on basis of digraphs theory and parallel computation. Changes proposed allow for parallelisation of previously sequential part of the algorithm, accurate estimation of number of solutions created and speed-up of both parts of the algorithm. Reduction of algorithm’s complexity is greatest for monomials consisting of only one variable and for one-variable polynomial a complete set of minimal solutions can be found as fast as in linearithmic time.