Chemical trees enumeration algorithms

In the chemical community the need for representing chemical structures within a given family and of efficiently enumerating these structures suggested the use of computers and the implementation of fast enumeration algorithms. This paper considers the isomeric acyclic structures focusing on the enumeration of the alkane molecular family. For this family, Trinajstić et al. (1991) devised an enumeration algorithm which is the most widely known and utilized nowadays. Kvasnička and Pospichal (1991) have proposed an algorithmic scheme which, from the computational complexity point of view, can prove to be more efficient than the Trinajstić one, nevertheless, this algorithm, to the best of our knowledge, has never been implemented. Indeed an efficient implementation requires the introduction of non trivial data structures and other computational tricks. The main contribution of this paper consists of the definition of the implementation details of Kvasnička-Pospichal's algorithm, in a comparison of Trinajstić's, Kvasnička-Pospichal's and two new algorithms, proposed here, in terms of both computational complexity analysis and running times.