Bidirectional search in a string with wavelet trees and bidirectional matching statistics

Searching for genes encoding microRNAs (miRNAs) is an important task in genome analysis. Because the secondary structure of miRNA (but not the sequence) is highly conserved, the genes encoding it can be determined by finding regions in a genomic DNA sequence that match the structure. It is known that algorithms using a bidirectional search on the DNA sequence for this task outperform algorithms based on unidirectional search. The data structures supporting a bidirectional search (affix trees and affix arrays), however, are rather complex and suffer from their large space consumption. Here, we present a new data structure called bidirectional wavelet index that supports bidirectional search with much less space. With this data structure, it is possible to search for candidates of RNA secondary structural patterns in large genomes, for example the complete human genome. Another important application of this data structure is short read alignment. As a second contribution, we show how bidirectional matching statistics can be computed in linear time.