Efficient Generation of Evolutionary Trees

For the purposes of phylogenetic analysis, it is assumed that the phylogenetic pattern of evolutionary history can be represented as a branching diagram like a tree, with the terminal branches (or leaves) linking the species being analyzed and the internal branches linking hypothesized ancestral species. To a mathematician, such a tree is simply a cycle-free connected graph, but to a biologist it represents a series of hypotheses about evolutionary events. In this paper we are concerned with generating all such probable evolutionary trees that will guide biologists to research in all biological subdisciplines. We give an algorithm to generate all evolutionary trees having n ordered species without repetition. We also find out an efficient representation of such evolutionary trees such that each tree is generated in constant time on average.