Eric Coissac
6acafa7f2c
Introduces a comprehensive documentation set covering theoretical foundations, CLI usage, installation, and system architecture. Adds MkDocs configuration and Makefile targets to generate, serve with live reload, and clean the documentation site. Includes citation styles and bibliography files for academic references.
25 lines
1.9 KiB
Markdown
25 lines
1.9 KiB
Markdown
# Kmers and super-kmers
|
|
|
|
## Kmers
|
|
|
|
A **kmer** is a DNA subsequence of fixed length $k$. Two constraints apply to $k$, both enforced when a command starts (an invalid value exits immediately with an error):
|
|
|
|
- $k \in [11, 31]$: long enough to be specific, short enough to fit in a single 64-bit word at 2 bits/base ($k \le 32$ is the hard limit; $k < 11$ gives insufficient specificity).
|
|
- $k$ **is odd**: an odd-length sequence can never equal its own reverse complement, so the two orientations of any kmer are always distinct. This is required for the canonical form (see [DNA encoding](encoding.md)) to be well defined.
|
|
|
|
## Super-kmers
|
|
|
|
A **super-kmer** is a maximal run of consecutive, overlapping kmers from a read that share the same canonical minimizer (see [Minimizer selection](minimizer_selection.md)). Each kmer in the run overlaps the next by $k-1$ nucleotides. A super-kmer is capped at 256 nucleotides; a longer run is split at that boundary.
|
|
|
|
For a random minimizer of length $m$ over kmers of length $k$, the expected length of a super-kmer is approximately [@Zheng2020-ji; @Golan2025-xf]:
|
|
|
|
$$L_{\text{nt}} \approx \frac{k-m+2}{2} + k - 1$$
|
|
|
|
For $k=31$, $m=13$ this is about 40 nucleotides; in practice super-kmers rarely exceed a few dozen nucleotides.
|
|
|
|
### Canonical super-kmers
|
|
|
|
A **canonical super-kmer** is the lexicographic minimum of a super-kmer and its reverse complement. When a read and its reverse complement are both encountered, they produce super-kmers that are reverse complements of each other; both reduce to the same canonical super-kmer, so a genomic region is represented once regardless of which strand was read.
|
|
|
|
Super-kmers are the unit of work used throughout construction and querying: sequences are decomposed into super-kmers first, and every downstream step (partition routing, deduplication, counting) operates on them rather than on individual kmers.
|