Traits of interval tree in solving blind search problems of finding a term in an ordered data set

Abstract

This paper investigates the traits of the interval tree in solving the blind-searched problems of finding uninformed terms in an ordered data set. It first proves several new properties of the interval tree and then shows that applying an interval tree to express data set results in half of the objective terms lying on the bottom level while another half lying on the levels over the bottom, and a bigger probability as well as half or less than half a amount of searching steps to find an objective term in comparison to conventional search strategies. Mathematical reasoning on the new properties of the interval tree plus conclusions related with the distribution of the objective terms on the interval tree is shown in detail and searching strategy is proposed in the end. The results in this paper are helpful for designing a searching algorithm.