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We consider the problem on constructing a binary search tree for an arbitrary set of binary words, which has found a wide use in informatics, biology, mineralogy, and other fields. It is known that the problem on constructing the tree of minimal cost is NP-complete; hence the problem arises to find simple algorithms which allow us to construct trees close to the optimal ones. In this paper we demonstrate that even simplest algorithm yields search trees which are close to the optimal ones in average, and prove that the mean number of nodes checked in the optimal tree differs from the natural lower bound, the binary logarithm of the number of words, by no more than 1.04.

An estimate of mean efficiency of search trees for arbitrary sets of binary words