A spread in PG(n,q) is a set of lines which partition the point set. A partition of the set of lines by spreads is called a parallelism. The numerous relations and applications of parallelisms determine a significant interest in the methods for their construction. We consider two different backtrack search algorithms which can be used for that purpose. The first one implies search on a set of spreads, and the second - on the lines of the projective space. The authors have used them for the classification of parallelisms invariant under definite automorphism groups. The present paper concerns the applicability of each of the two algorithms to cases with different peculiarities, and some ways to modify them for usage on parallel computers. Suitable examples are given.

https://link.springer.com/chapter/10.1007/978-3-030-79987-8_38