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, Trinajsti et al. (1991) devised an enumeration algorithm which is the most widely known and utilized nowadays. Kvasnika and Pospichal (1991) have proposed an algorithmic scheme which, from the computational complexity point of view, can prove to be more efficient than the Trinajsti 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 Kvasnika-Pospichals algorithm, in a comparison of Trinajstis, Kvasnika-Pospichals and two new algorithms, proposed here, in terms of both computational complexity analysis and running times.AMS classification: 05A15, 05C05, 05C30, 05C90Part of this work has been developed during a visit of the first two authors at the EPFL of Lausanne