A new algorithm for "the LCS problem" with application in compressing genome resequencing data.

Richard Beal,Aliya Farheen,Tazin Afrin,Donald Adjeroh

doi:10.1186/s12864-016-2793-0

Abstract

BackgroundThe longest common subsequence (LCS) problem is a classical problem in computer science, and forms the basis of the current best-performing reference-based compression schemes for genome resequencing data.MethodsFirst, we present a new algorithm for the LCS problem. Using the generalized suffix tree, we identify the common substrings shared between the two input sequences. Using the maximal common substrings, we construct a directed acyclic graph (DAG), based on which we determine the LCS as the longest path in the DAG. Then, we introduce an LCS-motivated reference-based compression scheme using the components of the LCS, rather than the LCS itself.ResultsOur basic scheme compressed the Homo sapiens genome (with an original size of 3,080,436,051 bytes) to 15,460,478 bytes. An improvement on the basic method further reduced this to 8,556,708 bytes, or an overall compression ratio of 360. This can be compared to the previous state-of-the-art compression ratios of 157 (Wang and Zhang, 2011) and 171 (Pinho, Pratas, and Garcia, 2011).ConclusionWe propose a new algorithm to address the longest common subsequence problem. Motivated by our LCS algorithm, we introduce a new reference-based compression scheme for genome resequencing data. Comparative results against state-of-the-art reference-based compression algorithms demonstrate the performance of the proposed method.

Highlights

The longest common subsequence (LCS) problem is a classical problem in computer science, and forms the basis of the current best-performing reference-based compression schemes for genome resequencing data
Recall that the parameter k is a type of threshold used by our compression scheme to determine whether it is more beneficial to encode a symbol verbatim or encode a common substrings (CSSs) as a triple
Our compression algorithm works on the longest previous factor (LPF) in a left-to-right fashion, selecting the leftmost CSS, say T[ i . . . i + l − 1] of length-(LPF[ i] = l), and determining whether to encode that CSS as a triple [and consider the CSS (T[ i + l . . . i + l + LPF[ i + l] −1] of length-LPF[ i + l])], or encode the first symbol (T[ i]) [and consider the CSS (T[ i + 1 . . . i + LPF[ i + 1] ] of length-LPF[ i + 1])]

Summary

Introduction

The longest common subsequence (LCS) problem is a classical problem in computer science, and forms the basis of the current best-performing reference-based compression schemes for genome resequencing data. An important approach to this problem is computing the longest common subsequence (LCS) between two strings S1 and S2, i.e. the longest ordered list of symbols common between S1 and S2. Biological applications of the LCS and similarity measurement are varied, from sequence alignment [5] in comparative genomics [6], to phylogenetic construction and analysis, to rapid search in huge biological sequences [7], to compression and efficient storage of the rapidly expanding genomic data sets [8, 9], to re-sequencing a set of strings given a target string [10], an important step in efficient genome assembly.

Methods

Results

Conclusion