These are not the k-mers you are looking for: efficient online k-mer counting using a probabilistic data structure
Qingpeng Zhang, Jason Pell, Rosangela Canino-Koning, Adina Chuang Howe, C. Titus Brown
(Submitted on 11 Sep 2013)

K-mer abundance analysis is widely used for many purposes in sequence analysis, including data preprocessing for de novo assembly, repeat detection, and sequencing coverage estimation. We present the khmer software package for fast and memory efficient online counting of k-mers in sequencing data sets. Unlike previous methods based on data structures such as hash tables, suffix arrays, and trie structures, khmer relies entirely on a simple probabilistic data structure, a CountMin Sketch. The CountMin Sketch permits online updating and retrieval of k-mer counts in memory which is necessary to support streaming k-mer analysis algorithms. On sparse data sets this data structure is considerably more memory efficient than any exact data structure. In exchange, the use of a CountMin Sketch introduces a systematic overcount for k-mers; moreover, only the counts, and not the k-mers, are stored. Here we analyze the speed, the memory usage, and the miscount rate of khmer for generating k-mer frequency distributions and retrieving k-mer counts for individual k-mers. We also compare the performance of khmer to several other k-mer counting packages, including Tallymer, Jellyfish, and DSK. Finally, we examine the effectiveness of profiling sequencing error, k-mer abundance trimming, and digital normalization of reads in the context of high khmer error rates. Khmer is implemented in C++ wrapped with a Python interface, offers a tested and robust API, and is freely available under the BSD license at github.com/ged-lab/khmer.