# scTurtle Algorithm for Kmer Counting

In our previous commentary on k-mer counting, one program was mentioned peripherally, because we knew little about it. On further reading, we find the paper worth mentioning in a separate commentary, because it brings a number of new concepts to bioinformatics.

In simple language, the approach can be described as ‘modified BFcounter’.

First we use a Bloom ?lter to identify the k-mers that were seen at least twice (with a small false positive rate). To count the frequency of these k-mers, we use an array of items containing a k-mer and its count. These are the two main components of our tool. Once the counts are computed, we can output the k-mers having frequency greater than the chosen cutoff.

The devil is, of course, in the details.

First, they use “Pattern-blocked Bloom Filter”. What is that? It is a new cache-efficient implementation for Bloom filters developed by a German group. The paper is a must-read.

A Bloom filter is a very compact data structure that supports approximate membership queries on a set, allowing false positives. We propose several new variants of Bloom filters and replacements with similar functionality. All of them have a better cache-efficiency and need less hash bits than regular Bloom filters. Some use SIMD functionality, while the others provide an even better space efficiency. As a consequence, we get a more flexible trade-off between false positive rate, space efficiency, cache-efficiency, hash-efficiency, and computational effort. We analyze the efficiency of Bloom filters and the proposed replacements in detail, in terms of the false positive rate, the number of expected cache misses, and the number of required hash bits. We also describe and experimentally evaluate the performance of highly-tuned implementations. For many settings, our alternatives perform better than the methods proposed so far.

The second innovation of the paper is a novel sort-and-count method. Is is similar to run-length encoding.

Counting frequencies with sorting and compaction

Counting frequencies with sorting and compaction Our next objective is to count the frequencies of the frequent k-mers. The basic idea is to store the frequent k-mers in an array A of size> n, where n is the number of frequent items. When this array fills up, we sort the items by the k-mer values. This places the items with the same k-mer next to each other in the array. Now, by making a linear traversal of the array, we can replace multiple items with the same k-mer with one item where a count field represents how many items were merged which is equal to how many times this k-mer was seen; see Figure 1. Note that, this is very similar to run length encoding.

The paper also claimed that DSK was not as fast as reported.

Rizk et al. (2013) claimed DSK to be faster than BFCounter, but on our machine, which had a 18TB Raid-6 storage system of 2TB SATA disks, it proved to be slower (1591 mins vs. 1012 mins for the GG dataset). Rizk et al. (2013) reported using more efficient storage systems (like SSD), the lack of which in our machine might explain DSKs poor performance in our experiments.

Not sure why they had that bad experience, because Titus Brown’s benchmarks found DSK faster than BFcounter. Titus Brown also found sTurtle as good as it claimed to be. So, it is definitely a top-rated kmer counter.