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docs: expand kmer indexing, filtering, and merging documentation
2026-06-04 21:27:01 +02:00
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<h1 id="approximate-evidence-fingerprint-based-index">Approximate evidence: fingerprint-based index</h1>
<h2 id="motivation">Motivation</h2>
<p><code>evidence.bin</code> maps each MPHF slot to the position of the k-mer that owns it,
enabling zero-FP verification. On the bacterial BCT dataset (2048 partitions,
k=31, ~33 M k-mers/partition) it accounts for 66 % of the lookup-layer footprint:</p>
<table>
<thead>
<tr>
<th>file</th>
<th>size/partition</th>
<th>fraction</th>
</tr>
</thead>
<tbody>
<tr>
<td>evidence.bin</td>
<td>132 MB</td>
<td>66 %</td>
</tr>
<tr>
<td>unitigs.bin</td>
<td>58 MB</td>
<td>29 %</td>
</tr>
<tr>
<td>mphf.bin</td>
<td>10 MB</td>
<td>5 %</td>
</tr>
</tbody>
</table>
<p><code>evidence.bin</code> is a bijection from MPHF-space to unitig-position-space and
costs at minimum ⌈log₂ N⌉ bits per slot — an information-theoretic floor with
only ~22 % packing headroom. Compression is not a path to elimination.</p>
<p>The approximate index replaces <code>evidence.bin</code> + <code>unitigs.bin.idx</code> with a
<code>fingerprint.bin</code> file. The MPHF and <code>unitigs.bin</code> are kept unchanged. Set
operations still require an exact index; the approximate index targets query
workloads that can tolerate a bounded false-positive rate.</p>
<hr />
<h2 id="the-findere-model">The Findere model</h2>
<p>A B-bit fingerprint stored per MPHF slot provides the discrimination that
<code>evidence.bin</code> would otherwise provide through full k-mer reconstruction.</p>
<p>For a foreign k-mer query, the MPHF maps it to some slot <code>s</code>. The fingerprint
stored at <code>s</code> belongs to the legitimate k-mer at that slot. The FP event is:</p>
<div class="highlight"><pre><span></span><code>P(FP per k-mer) = 1 / 2^b
</code></pre></div>
<p>The Findere trick reduces the indexed k-mer size. When the user specifies k_user
and z, the index physically stores k-mers of size <code>s = k_user − z + 1</code>. At query
time, the same s-mer size is used. After collecting per-position s-mer results
over the full query sequence, a sliding window of size z aggregates z consecutive
s-mer hits into one confirmed k_user-mer hit, reducing the per-window FP rate:</p>
<div class="highlight"><pre><span></span><code>P(FP per k_user-mer) = 1 / 2^(b·z)
</code></pre></div>
<p><code>IndexConfig::kmer_size</code> stores <code>s = k_user − z + 1</code>, not k_user. Both indexing
and querying use this stored size via <code>set_k(idx.kmer_size())</code>.</p>
<p>Parameters b and z are stored in <code>layer_meta.json</code> (<code>EvidenceKind::Approx { b, z }</code>).</p>
<hr />
<h2 id="fingerprintvec-on-disk"><code>FingerprintVec</code> on disk</h2>
<p><code>fingerprint.bin</code> layout:</p>
<div class="highlight"><pre><span></span><code>magic: b&quot;FPVF&quot; (4 bytes)
b: u8 (bits per slot, 1..=64)
padding: [0u8; 3]
n: u64 LE (number of slots)
data: packed bits, ceil(n·b/8) bytes, Lsb0 order
</code></pre></div>
<p><code>FingerprintVec</code> is memory-mapped. The match check against a query k-mer:</p>
<div class="highlight"><pre><span></span><code><span class="k">fn</span><span class="w"> </span><span class="nf">matches</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">slot</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">fingerprint</span><span class="p">:</span><span class="w"> </span><span class="kt">u64</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="n">slot</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="p">(</span><span class="n">fingerprint</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">mask</span><span class="p">)</span>
<span class="p">}</span>
</code></pre></div>
<p><code>build_approx_evidence</code> iterates <code>unitigs.bin</code> sequentially, writes
<code>kmer.seq_hash()</code> into the slot assigned by the MPHF, then saves <code>fingerprint.bin</code>
and <code>layer_meta.json</code>. No <code>.idx</code> file is produced; random access into
<code>unitigs.bin</code> is not needed.</p>
<p>At build time, <code>find_approx</code> in <code>MphfLayer</code>:</p>
<div class="highlight"><pre><span></span><code><span class="kd">let</span><span class="w"> </span><span class="n">slot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">mphf</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="o">&amp;</span><span class="n">kmer</span><span class="p">.</span><span class="n">raw</span><span class="p">());</span>
<span class="k">if</span><span class="w"> </span><span class="n">fingerprint</span><span class="p">.</span><span class="n">matches</span><span class="p">(</span><span class="n">slot</span><span class="p">,</span><span class="w"> </span><span class="n">kmer</span><span class="p">.</span><span class="n">seq_hash</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">slot</span><span class="p">)</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}</span>
</code></pre></div>
<hr />
<h2 id="evidencekind-and-metadata"><code>EvidenceKind</code> and metadata</h2>
<p><code>layer_meta.json</code> records which evidence bundle is present:</p>
<div class="highlight"><pre><span></span><code><span class="k">pub</span><span class="w"> </span><span class="k">enum</span><span class="w"> </span><span class="nc">EvidenceKind</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">Exact</span><span class="p">,</span>
<span class="w"> </span><span class="n">Approx</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="kt">u8</span><span class="p">,</span><span class="w"> </span><span class="n">z</span><span class="p">:</span><span class="w"> </span><span class="kt">u8</span><span class="w"> </span><span class="p">},</span>
<span class="p">}</span>
</code></pre></div>
<p><code>MphfLayer::open</code> reads this tag and dispatches <code>find</code> to <code>find_exact</code> or
<code>find_approx</code> transparently. <code>find_exact</code> panics on an approximate layer;
<code>find_approx</code> panics on an exact layer — mode mixing is a programming error.</p>
<hr />
<h2 id="parameter-resolution-resolve_approx_params">Parameter resolution (<code>resolve_approx_params</code>)</h2>
<p>The identity <code>b·z = ⌈−log₂(fp)⌉</code> lets any two of (b, z, fp) derive the third.
<code>resolve_approx_params</code> implements a 2-of-3 rule with conservative ceiling
rounding:</p>
<table>
<thead>
<tr>
<th>given</th>
<th>derived</th>
</tr>
</thead>
<tbody>
<tr>
<td>b, z</td>
<td>fp = 1/2^(b·z)</td>
</tr>
<tr>
<td>z, fp</td>
<td>b = ⌈−log₂(fp) / z⌉</td>
</tr>
<tr>
<td>b, fp</td>
<td>z = ⌈−log₂(fp) / b⌉</td>
</tr>
<tr>
<td>z only</td>
<td>b = 8 (default), fp derived</td>
</tr>
<tr>
<td>b only</td>
<td>z = 1 (default), fp derived</td>
</tr>
<tr>
<td>fp only</td>
<td>b = 8 (default), z derived</td>
</tr>
<tr>
<td>none</td>
<td>b = 8, z = 1, fp = 1/256</td>
</tr>
</tbody>
</table>
<p>When all three are given, b and z are authoritative and fp is recomputed.</p>
<hr />
<h2 id="cli-flags">CLI flags</h2>
<p>Both <code>index</code> and <code>reindex</code> accept the same flags:</p>
<table>
<thead>
<tr>
<th>flag</th>
<th>type</th>
<th>meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>--approx</code></td>
<td>bool</td>
<td>enable fingerprint evidence</td>
</tr>
<tr>
<td><code>--evidence-bits</code> (<code>b</code>)</td>
<td>u8</td>
<td>fingerprint bits per slot</td>
</tr>
<tr>
<td><code>-z</code></td>
<td>u8</td>
<td>Findere z parameter</td>
</tr>
<tr>
<td><code>--fp</code></td>
<td>f64</td>
<td>target FP rate per z-window</td>
</tr>
<tr>
<td><code>--block-size</code></td>
<td>usize</td>
<td>unitig block size for exact <code>.idx</code>; ignored in approx mode</td>
</tr>
</tbody>
</table>
<p><code>--approx</code> must be set explicitly; the other three flags are optional and
resolved by the 2-of-3 rule. Omitting all three produces b=8, z=1.</p>
<hr />
<h2 id="reindex-command"><code>reindex</code> command</h2>
<p><code>reindex</code> converts an existing index between exact and approximate evidence
in-place across all partitions and layers, running partitions in parallel via
Rayon.</p>
<p>Conversion to approximate (<code>--approx</code>):</p>
<ul>
<li>Builds <code>fingerprint.bin</code> from <code>unitigs.bin</code> + <code>mphf.bin</code>.</li>
<li>Removes <code>evidence.bin</code> and <code>unitigs.bin.idx</code>.</li>
<li>Updates <code>layer_meta.json</code> with <code>EvidenceKind::Approx { b, z }</code>.</li>
</ul>
<p>Conversion to exact (default, no <code>--approx</code>):</p>
<ul>
<li>Builds <code>evidence.bin</code> + <code>unitigs.bin.idx</code> from <code>unitigs.bin</code> + <code>mphf.bin</code>.</li>
<li>Removes <code>fingerprint.bin</code>.</li>
<li>Updates <code>layer_meta.json</code> with <code>EvidenceKind::Exact</code>.</li>
</ul>
<p>The root <code>index.meta</code> is updated with the new evidence kind on success.
<code>mphf.bin</code> and <code>unitigs.bin</code> are never modified.</p>
<hr />
<h2 id="estimate-command"><code>estimate</code> command</h2>
<p><code>estimate</code> is a dry-run that resolves and prints (b, z, fp) without touching
any index. It accepts the same <code>--evidence-bits</code>, <code>-z</code>, and <code>--fp</code> flags and
additionally accepts <code>-k</code> to display the effective indexed k-mer length:</p>
<div class="highlight"><pre><span></span><code>k (user): 31
k (indexed, s=k-z+1): 27
z: 5
evidence bits (b): 8
FP per s-mer: 3.906e-3 (1/2^8)
FP per k-mer window: 9.537e-7 (1/2^(8·5))
</code></pre></div>
<p>Useful for choosing parameters before committing to an index build.</p>
</article>
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