Localized suffix array and its application to genome mapping problems for paired-end short reads.

We introduce a new data structure, a localized suffix array, based on which occurrence information is dynamically represented as the combination of global positional information and local lexicographic order information in text search applications. For the search of a pair of words within a given distance, many candidate positions that share a coarse-grained global position can be compactly represented in term of local lexicographic orders as in the conventional suffix array, and they can be simultaneously examined for violation of the distance constraint at the coarse-grained resolution. Trade-off between the positional and lexicographical information is progressively shifted towards finer positional resolution, and the distance constraint is reexamined accordingly. Thus the paired search can be efficiently performed even if there are a large number of occurrences for each word. The localized suffix array itself is in fact a reordering of bits inside the conventional suffix array, and their memory requirements are essentially the same. We demonstrate an application to genome mapping problems for paired-end short reads generated by new-generation DNA sequencers. When paired reads are highly repetitive, it is time-consuming to naïvely calculate, sort, and compare all of the coordinates. For a human genome re-sequencing data of 36 base pairs, more than 10 times speedups over the naïve method were observed in almost half of the cases where the sums of redundancies (number of individual occurrences) of paired reads were greater than 2,000.