Improved approximate common interval

The approximate common interval (ACI) problem, where the multiple genome strings are required to be compared to all other character sets of the other string is discussed. Genomes are considered as strings, with possible repeats of symbols representing paralogous genes, and detect the gene clusters by modeling gene intervals by the set of characters. A specific number of time algorithm that locates all intervals of two strings share the same character set, which also represents the number of the strings. This approximate common interval (ACI) problem for a specific number of strings can be solved in time and space by considering a finite length of every string. A procedure for extracting all maximal character sets of the input strings, and the ACI problem for a single input string and multiple input strings are studied. Graphic representation shows provides a simple and versatile algorithm, supporting the approximate common interval problem.