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Graph presentation of binary strings

Gjonbalaj Q. D., Hamiti V. R.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 2

17--27

This article is motivated by the problem of finding a graph, which operates on the principle of the Hasse diagram. In the present article, the Hasse diagram technique (HDT) was applied to relate binary string sets with graph theory. We investigate this relation in detail and propose a new graph, the so-called 2n-Parallel Graph (2nPG), and an efficient pseudo code that decompresses a given binary string set to its elements. The goal of this pseudo code is its application in determining the number of strings with a certain number of first bits consecutive 1’s (0’s). This pseudocode is also responsible for the solution of several combinatorial problems on a certain binary string. Furthermore, our results are valid for any string length.