Genome Homology Visualization by Short Similar Substring Enumeration (Acceleration and Visualization of Computation for Enumeration Problems)

Finding similar substrings/substructures is a central task in analyzing huge amounts of genome data.In the sense of complexity theory, the existence of polynomial time algorithms for such problems is usually trivial since the number of substrings is bounded by the square of their lengths.However, straightforward algorithms do not work for practical huge databases because of their computation time of high degree order.This paper addresses the problems of finding pairs of strings with small Hamming distances from huge databa.es composed of short strings of a fixed length.Using this, we compare two genomc scqucnces by solving this problcm for all the fixed- length substrings taken from the sequences.We focus on the practical efficiency of algorithms, and propose an algorithm running in almost linear tlme of the database size.When there are so many similar pairs so that the visualization is impossible, we propose to use a filtering algorithm to remove the pairs which are not parts of similar long sequences.Computational experiments for genome sequcnces show the efficiency of thc method.An implementation is available at the author's homepagel 1 IntroductionIn this paper, we consider the problem of enumerating all pairs of similar strings in a set $S$ of strings of the same length $l$ .We can approach to general substring comparison problems through this problem sinoe such non-short similar strings must include several such short similar substrings.As a similarity measure, we use Hamming distance.Thus the definition of the problem is as follows.Short Hamming Distance String Pair Enumeration Problem Input: a set $S$ of strings of the same length $l$ , a distance threshold $d$ Output: all pairs of strings $S_{1}$ and $S_{2}$ such that the Hamming distance between $S_{1}$ and $S_{2}$ is at most $d$ .We here call a pair of strings with Hamming distance at most $d$ similar string pair.We consider the

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