Eric Coissac
27f5e88a7b
Replace raw SuperkMer routing with a new RoutableSuperKimer type that embeds canonical sequences and precomputed minimizers, enabling direct partition routing via hash. Update the build pipeline to yield RoutableSuperKmers throughout (builder, scatterer), refactor FASTA/unitig export commands to use the new type and compressed outputs (.fasta.gz, .unitigs.fasta.zst), revise SuperKmer header to store n_kmers instead of seql (avoiding 256-byte wrap), and update documentation to reflect minimizer-based theory, two evidence-encoding strategies for unitig-MPHF indexing (global offset vs. ID+rank), and the new obipipeline library architecture with parallel workers, biased scheduling, and error handling.
994 lines
21 KiB
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994 lines
21 KiB
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Kmers and super-kmers
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DNA encoding
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Entropy filter
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Minimizer selection
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Partitioning architecture
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Partitioning architecture
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Why hashing is necessary
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SuperKmer
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Kmer
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Chunk reader
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Construction pipeline
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<span class="md-ellipsis">
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obipipeline library
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On-disk storage
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MPHF selection
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Unitig evidence encoding
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Architecture
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Sequences
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Why hashing is necessary
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Parameter choices
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<h1 id="partitioning-and-indexing-architecture">Partitioning and indexing architecture</h1>
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<p>The canonical minimizer of a super-kmer is hashed to produce a <strong>p-bit routing value</strong> (p is a collection-level parameter):</p>
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<div class="highlight"><pre><span></span><code>canonical minimizer → hash(minimizer) → p-bit value → PART → partition directory
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</code></pre></div>
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<p>PART is computed once at phase 1 to open the correct partition file, then discarded. It is recomputed on the fly at query time. It is never stored in the super-kmer header.</p>
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<p>Each partition holds one MPHF instance (phase 6) that indexes kmers as plain u64 values — the minimizer plays no role inside the partition.</p>
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<h2 id="why-hashing-is-necessary">Why hashing is necessary</h2>
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<p>The canonical minimizer is an m-mer (m ∈ {9, 11, 13, 15}), encoded in 2m bits (18 to 30 bits). Its distribution over the <span class="arithmatex">\(4^m\)</span> possible values is <strong>not uniform</strong>: because the minimizer is the lexicographic minimum of a window of m-mers, small values are systematically over-represented (Golan & Shur 2025; Kille <em>et al.</em> 2023; Pan & Reinert 2024; Zheng <em>et al.</em> 2020, 2021)<sup id="fnref:Zheng2020-ji"><a class="footnote-ref" href="#fn:Zheng2020-ji">1</a></sup> <sup id="fnref:Zheng2021-cc"><a class="footnote-ref" href="#fn:Zheng2021-cc">2</a></sup> <sup id="fnref:Pan2024-hb"><a class="footnote-ref" href="#fn:Pan2024-hb">3</a></sup> <sup id="fnref:Kille2023-px"><a class="footnote-ref" href="#fn:Kille2023-px">4</a></sup> <sup id="fnref:Golan2025-xf"><a class="footnote-ref" href="#fn:Golan2025-xf">5</a></sup>. Routing directly by the raw minimizer value would produce severely unbalanced partitions.</p>
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<p>A hash function with good avalanche properties redistributes this skewed distribution uniformly over the <span class="arithmatex">\(2^p\)</span> partition slots. The key reason this works well is the <strong>entropy gap</strong>: p is chosen to be much smaller than 2m, so the hash compresses many distinct minimizer values into each partition slot. Even under strong bias in the minimizer distribution, as long as its effective entropy exceeds p bits — which holds comfortably since the set of distinct minimizers in any real dataset is far larger than <span class="arithmatex">\(2^p\)</span> — the load imbalance across partitions is negligible.</p>
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<h2 id="parameter-choices">Parameter choices</h2>
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<table>
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<thead>
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<tr>
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<th>m</th>
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<th>2m (bits)</th>
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<th>Typical p</th>
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<th>Partitions</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>9</td>
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<td>18</td>
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<td>6–8</td>
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<td>64–256</td>
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</tr>
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<tr>
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<td>11</td>
|
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<td>22</td>
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<td>8–10</td>
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<td>256–1 024</td>
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</tr>
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<tr>
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<td>13</td>
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<td>26</td>
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<td>10–12</td>
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<td>1 024–4 096</td>
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</tr>
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<tr>
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<td>15</td>
|
||
<td>30</td>
|
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<td>10–14</td>
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<td>1 024–16 384</td>
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</tr>
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</tbody>
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</table>
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<p>The hard constraint is p ≤ 2m: one cannot extract more bits of uniform randomness from a source than it contains. In practice p is chosen well below 2m, leaving a large entropy margin that absorbs the minimizer bias. For k=31, m=13, p=10: 1 024 partitions with comfortable balance.</p>
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<div class="footnote">
|
||
<hr />
|
||
<ol>
|
||
<li id="fn:Zheng2020-ji">
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||
<p>Zheng, H., Kingsford, C. & Marçais, G. (2020). <a href="https://doi.org/10.1093/bioinformatics/btaa472">Improved design and analysis of practical minimizers</a>. <em>Bioinformatics (Oxford, England)</em>, 36, i119--i127. <a class="footnote-backref" href="#fnref:Zheng2020-ji" title="Jump back to footnote 1 in the text">↩</a></p>
|
||
</li>
|
||
<li id="fn:Zheng2021-cc">
|
||
<p>Zheng, H., Kingsford, C. & Marçais, G. (2021). <a href="https://doi.org/10.1093/bioinformatics/btab313">Sequence-specific minimizers via polar sets</a>. <em>Bioinformatics (Oxford, England)</em>, 37, i187--i195. <a class="footnote-backref" href="#fnref:Zheng2021-cc" title="Jump back to footnote 2 in the text">↩</a></p>
|
||
</li>
|
||
<li id="fn:Pan2024-hb">
|
||
<p>Pan, C. & Reinert, K. (2024). <a href="https://doi.org/10.1093/bioinformatics/btae045">A simple refined DNA minimizer operator enables 2-fold faster computation</a>. <em>Bioinformatics (Oxford, England)</em>, 40. <a class="footnote-backref" href="#fnref:Pan2024-hb" title="Jump back to footnote 3 in the text">↩</a></p>
|
||
</li>
|
||
<li id="fn:Kille2023-px">
|
||
<p>Kille, B., Garrison, E., Treangen, T.J. & Phillippy, A.M. (2023). <a href="https://doi.org/10.1093/bioinformatics/btad512">Minmers are a generalization of minimizers that enable unbiased local jaccard estimation</a>. <em>Bioinformatics (Oxford, England)</em>, 39. <a class="footnote-backref" href="#fnref:Kille2023-px" title="Jump back to footnote 4 in the text">↩</a></p>
|
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</li>
|
||
<li id="fn:Golan2025-xf">
|
||
<p>Golan, S. & Shur, A.M. (2025). <a href="https://doi.org/10.1007/978-3-031-82670-2\_25">Expected density of random minimizers</a>. In: <em>Lecture notes in computer science</em>, Lecture notes in computer science. Springer Nature Switzerland, Cham, pp. 347--360. <a class="footnote-backref" href="#fnref:Golan2025-xf" title="Jump back to footnote 5 in the text">↩</a></p>
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