KmerEstimate: A Streaming Algorithm for Estimating k-mer Counts with Optimal Space Usage

Abstract

The frequency distribution of k-mers (substrings of length k in a DNA/RNA sequence) is very useful for many bioinformatics applications that use next-generation sequencing (NGS) data. Some examples of these include de Bruijn graph based assembly, read error correction, genome size prediction, and digital normalization. In developing tools for such applications, counting (or estimating) k-mers with low frequency is a pre-processing phase. However, computing k-mer frequency histogram becomes computationally challenging for large-scale genomic data. We present KmerEstimate, a \em streaming algorithm that approximates the count of k-mers with a given frequency in a genomic data set. Our algorithm is based on a well known adaptive sampling based streaming algorithm due to Bar-Yossef et al. for approximating distinct elements in a data stream. We implemented and tested our algorithm on several data sets. The results of our algorithm are better than that of other streaming approaches used so far for this problem (notably $ntCard$, the state-of-the-art streaming approach) and is within 0.6% error rate. It uses less memory than $ntCard$ as the sample size is almost 85% less than that of $ntCard$. In addition, our algorithm has provable approximation and space usage guarantees. We also show certain space complexity lower bounds. The source code of our algorithm is available at \urlhttps://github.com/srbehera11/KmerEstimate. We present KmerEstimate, a \em streaming algorithm that approximates the count of k-mers with a given frequency in a genomic data set. Our algorithm is based on a well known adaptive sampling based streaming algorithm due to Bar-Yossef et al. for approximating distinct elements in a data stream. We implemented and tested our algorithm on several data sets. The results of our algorithm are better than that of other streaming approaches used so far for this problem (notably $ntCard$, the state-of-the-art streaming approach) and are within 0.6% error rate. It uses less memory than $ntCard$ as the sample size is almost 85% less than that of $ntCard$. In addition, our algorithm has provable approximation and space usage guarantees. We also show certain space complexity lower bounds. The source code of our algorithm is available at \urlhttps://github.com/srbehera11/KmerEstimate.