Optimum Search Schemes for Approximate String Matching Using Bidirectional FM-Index

TL;DR

This paper introduces a mixed integer programming approach to optimize search schemes for approximate string matching with bidirectional FM-indexes, significantly improving search speed and efficiency in bioinformatics applications.

Contribution

It presents the first MIP-based method to find optimal search schemes for approximate matching, enhancing performance over previous ad-hoc solutions.

Findings

Optimal search schemes significantly speed up approximate matching.

Approximate matching of 101-bp reads with two errors is 35 times faster.

Search time with optimal schemes is comparable to state-of-the-art aligners.

Abstract

Finding approximate occurrences of a pattern in a text using a full-text index is a central problem in bioinformatics and has been extensively researched. Bidirectional indices have opened new possibilities in this regard allowing the search to start from anywhere within the pattern and extend in both directions. In particular, use of search schemes (partitioning the pattern and searching the pieces in certain orders with given bounds on errors) can yield significant speed-ups. However, finding optimal search schemes is a difficult combinatorial optimization problem. Here for the first time, we propose a mixed integer program (MIP) capable to solve this optimization problem for Hamming distance with given number of pieces. Our experiments show that the optimal search schemes found by our MIP significantly improve the performance of search in bidirectional FM-index upon previous ad-hoc solutions. For example, approximate matching of 101-bp Illumina reads (with two errors) becomes 35 times faster than standard backtracking. Moreover, despite being performed purely in the index, the running time of search using our optimal schemes (for up to two errors) is comparable to the best state-of-the-art aligners, which benefit from combining search in index with in-text verification using dynamic programming. As a result, we anticipate a full-fledged aligner that employs an intelligent combination of search in the bidirectional FM-index using our optimal search schemes and in-text verification using dynamic programming outperforms today's best aligners. The development of such an aligner, called FAMOUS (Fast Approximate string Matching using OptimUm search Schemes), is ongoing as our future work.