Eric Coissac
f36b095ce2
Formalize the two-phase MPHF indexing architecture and update Phase 6 to use `evidence.bin` for direct kmer extraction. Simplify the evidence and unitig storage layouts to flat packed formats enabling O(1) random access. Introduce aggregation traits (`ColumnWeights`, `CountPartials`, `BitPartials`) to support additive distance metric decomposition across partitions. Narrow the documented scope from metagenomic to individual genome datasets, and replace speculative open questions with concrete implementation specifications.
1404 lines
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1404 lines
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Kmers and super-kmers
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DNA encoding
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Minimizer selection
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Chunk reader
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MPHF selection
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MPHF selection
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Phase 1 — provisional MPHF + kmer spectrum
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Phase 2 — definitive MPHF
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MPHF candidates
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MPHF choice per phase
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ptr_hash configuration (phase 2)
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
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<a href="#multilayer-index-architecture" class="md-nav__link">
|
||
<span class="md-ellipsis">
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Multilayer index architecture
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Layer structure
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Membership verification
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</li>
|
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<li class="md-nav__item">
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Query algorithm
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#merging-layers" class="md-nav__link">
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<span class="md-ellipsis">
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Merging layers
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Unitig evidence encoding
|
||
|
||
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||
|
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</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
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obilayeredmap crate
|
||
|
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|
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</span>
|
||
|
||
|
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|
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</a>
|
||
</li>
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||
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<a href="../persistent_compact_int_vec/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
||
|
||
PersistentCompactIntVec
|
||
|
||
|
||
|
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</span>
|
||
|
||
|
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|
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</a>
|
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|
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PersistentBitVec
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
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|
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</a>
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Architecture
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Sequences
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Kmer index
|
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Phase 1 — provisional MPHF + kmer spectrum
|
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Phase 2 — definitive MPHF
|
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MPHF candidates
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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MPHF choice per phase
|
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|
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</a>
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|
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<li class="md-nav__item">
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<span class="md-ellipsis">
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Space at scale
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</a>
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<li class="md-nav__item">
|
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<a href="#ptr_hash-configuration-phase-2" class="md-nav__link">
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ptr_hash configuration (phase 2)
|
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</a>
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|
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Layer structure
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<a href="#query-algorithm" class="md-nav__link">
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Query algorithm
|
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</a>
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</li>
|
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<li class="md-nav__item">
|
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<a href="#merging-layers" class="md-nav__link">
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Merging layers
|
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</div>
|
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<div class="md-content" data-md-component="content">
|
||
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="mphf-selection-two-phase-indexing-architecture">MPHF selection — two-phase indexing architecture</h1>
|
||
<h2 id="why-two-phases-are-needed">Why two phases are needed</h2>
|
||
<p>Kmer indexing per partition proceeds in two phases. The separation is necessary because the exact number of surviving unique kmers is not known until after counting and filtering low-abundance kmers.</p>
|
||
<h3 id="phase-1-provisional-mphf-kmer-spectrum">Phase 1 — provisional MPHF + kmer spectrum</h3>
|
||
<p>Implemented in <code>obikpartitionner::KmerPartition::count_kmer()</code>.</p>
|
||
<ol>
|
||
<li><strong>Pass 1</strong>: read the dereplicated superkmer file; enumerate all unique canonical kmers into a <code>HashSet</code>. Exact count known after this pass.</li>
|
||
<li><strong>Build a provisional MPHF</strong> (<code>GOFunction</code> from the <code>ph</code> crate) over the exact kmer set. Produces <code>mphf1.bin</code>.</li>
|
||
<li><strong>Create <code>counts1.bin</code></strong>: one zero-initialised <code>u32</code> per MPHF slot (mmap'd).</li>
|
||
<li><strong>Pass 2</strong>: re-read the dereplicated file; for each kmer, query <code>mphf1.get(kmer)</code> and atomically accumulate the superkmer count into <code>counts1[slot]</code>.</li>
|
||
<li><strong>Build kmer frequency spectrum</strong> from <code>counts1</code>: histogram <code>{count → n_kmers}</code>, totals f0 (distinct kmers) and f1 (total abundance). Written to <code>kmer_spectrum_raw.json</code> per partition, then merged globally.</li>
|
||
</ol>
|
||
<p>Files produced per partition:</p>
|
||
<div class="highlight"><pre><span></span><code>part_XXXXX/
|
||
mphf1.bin — GOFunction (provisional MPHF, discarded after phase 2)
|
||
counts1.bin — [u32; n_kmers] kmer counts, mmap'd
|
||
kmer_spectrum_raw.json — local frequency spectrum
|
||
</code></pre></div>
|
||
<h3 id="phase-2-definitive-mphf">Phase 2 — definitive MPHF</h3>
|
||
<p>After filtering (applying a min-count threshold derived from the spectrum) and building the local De Bruijn graph + unitigs (see <a href="../pipeline/">Construction pipeline</a>), the exact filtered kmer set is available via <code>unitigs.bin</code>.</p>
|
||
<p><code>MphfLayer::build</code> is called on the unitig file:</p>
|
||
<ol>
|
||
<li><strong>Pass 1</strong>: iterate all canonical kmers from <code>unitigs.bin</code> in parallel, build and store <code>mphf.bin</code> (ptr_hash).</li>
|
||
<li><strong>Pass 2</strong>: iterate sequentially, fill <code>evidence.bin</code>, call the mode-specific <code>fill_slot</code> callback.</li>
|
||
</ol>
|
||
<p><code>mphf1.bin</code> and <code>counts1.bin</code> are no longer needed after phase 2 and can be deleted.</p>
|
||
<hr />
|
||
<h2 id="mphf-candidates">MPHF candidates</h2>
|
||
<p><strong>boomphf</strong> (BBHash algorithm, maintained by 10X Genomics):</p>
|
||
<ul>
|
||
<li>~3.7 bits/key; mature crate, used in production bioinformatics (Pufferfish, Piscem)</li>
|
||
<li>Supports streaming construction (no exact count needed)</li>
|
||
<li>Drawback: largest space footprint; streaming advantage is irrelevant at phase 2 since the exact count is available</li>
|
||
</ul>
|
||
<p><strong>ptr_hash</strong> (PtrHash algorithm, Groot Koerkamp, SEA 2025):</p>
|
||
<ul>
|
||
<li>~2.4 bits/key; fastest queries (≥2.1× over alternatives, 8–12 ns/key for u64) and fastest construction (≥3.1×)</li>
|
||
<li>Requires exact key count at construction — available at both phases after pass 1</li>
|
||
<li>Published February 2025; accepted given performance profile and the fact that each MPHF is independently rebuildable from its unitig file</li>
|
||
</ul>
|
||
<p><strong>FMPH/FMPHGO</strong> (<code>ph</code> crate, Beling, ACM JEA 2023):</p>
|
||
<ul>
|
||
<li>~2.1 bits/key — most compact; good query speed; deterministic construction</li>
|
||
<li>Works well from an exact or slightly overestimated count</li>
|
||
<li><code>GOFunction</code> (group-oriented variant) is the specific type used</li>
|
||
</ul>
|
||
<h2 id="mphf-choice-per-phase">MPHF choice per phase</h2>
|
||
<p><strong>Phase 1</strong> (provisional, discarded after spectrum computation): <code>ph::fmph::GOFunction</code>. Compact, fast to build from the exact post-dedup kmer set. Query speed is secondary — the structure is only used during pass 2 of <code>count_kmer</code>.</p>
|
||
<p><strong>Phase 2</strong> (persistent, queried repeatedly): <strong>ptr_hash</strong>. Exact key count is available from the unitig index; ptr_hash query speed (≥2.1×) and construction speed (≥3.1× over FMPH) are the decisive factors. The 2.4 bits/key overhead is acceptable.</p>
|
||
<p>boomphf is eliminated: largest space overhead, streaming advantage does not apply.</p>
|
||
<hr />
|
||
<h2 id="space-at-scale">Space at scale</h2>
|
||
<p>For 1 024 partitions × 100 M kmers/partition (phase 2 index, after filtering):</p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>MPHF</th>
|
||
<th>bits/key</th>
|
||
<th>Total MPHF size</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>boomphf</td>
|
||
<td>3.7</td>
|
||
<td>~47 GB</td>
|
||
</tr>
|
||
<tr>
|
||
<td>ptr_hash</td>
|
||
<td>2.4</td>
|
||
<td>~31 GB</td>
|
||
</tr>
|
||
<tr>
|
||
<td>FMPH</td>
|
||
<td>2.1</td>
|
||
<td>~27 GB</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p>For a human genome at 30× coverage with 1 024 partitions, realistic partition sizes are 3–30 M unique kmers → 1–8 MB per phase-2 MPHF, well within RAM.</p>
|
||
<hr />
|
||
<h2 id="ptr_hash-configuration-phase-2">ptr_hash configuration (phase 2)</h2>
|
||
<div class="highlight"><pre><span></span><code><span class="k">type</span><span class="w"> </span><span class="nc">Mphf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PtrHash</span><span class="o"><</span>
|
||
<span class="w"> </span><span class="kt">u64</span><span class="p">,</span><span class="w"> </span><span class="c1">// key: canonical kmer raw encoding</span>
|
||
<span class="w"> </span><span class="n">CubicEps</span><span class="p">,</span><span class="w"> </span><span class="c1">// bucket fn: 2.4 bits/key, λ=3.5, α=0.99</span>
|
||
<span class="w"> </span><span class="n">CachelineEfVec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">CachelineEf</span><span class="o">>></span><span class="p">,</span><span class="w"> </span><span class="c1">// remap: 11.6 bits/entry (Elias-Fano)</span>
|
||
<span class="w"> </span><span class="n">Xx64</span><span class="p">,</span><span class="w"> </span><span class="c1">// hasher: XXH3-64 with seed</span>
|
||
<span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="kt">u8</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="c1">// pilots</span>
|
||
<span class="o">></span><span class="p">;</span>
|
||
</code></pre></div>
|
||
<p><strong>Hasher — <code>Xx64</code></strong>: canonical kmer raw values are left-aligned u64 with structural zeros in low bits (42 zeros for k=11, 2 zeros for k=31). <code>FxHash</code> (single multiply) distributes these poorly; <code>Xx64</code> (XXH3-64, seeded) handles structured input correctly.</p>
|
||
<p><strong>Bucket function — <code>CubicEps</code></strong>: λ=3.5, α=0.99. Balanced tradeoff: 2× slower construction than <code>Linear/λ=3.0</code>, 20% less space. <code>default_compact</code> (λ=4.0) saves a further 12.5% at 2× more construction time — not chosen.</p>
|
||
<p><strong>Remap — <code>CachelineEfVec</code></strong>: Elias-Fano variant packing 44 sorted 40-bit values per 64-byte cacheline (11.6 bits/value vs 32 for <code>Vec<u32></code>). One cacheline per query; space win dominates at billion-scale key counts.</p>
|
||
<hr />
|
||
<h2 id="multilayer-index-architecture">Multilayer index architecture</h2>
|
||
<h3 id="layer-structure">Layer structure</h3>
|
||
<p>Each layer is a self-contained unit. See <a href="../obilayeredmap/">obilayeredmap</a> for the full on-disk layout. The MPHF-relevant files are:</p>
|
||
<div class="highlight"><pre><span></span><code>layer_i/
|
||
unitigs.bin — packed 2-bit nucleotide sequences (kmer evidence)
|
||
mphf.bin — ptr_hash phase-2 MPHF
|
||
evidence.bin — n × u32: (chunk_id: 25 bits | rank: 7 bits) per slot
|
||
</code></pre></div>
|
||
<p>Layers are <strong>disjoint</strong>: a canonical kmer belongs to exactly one layer. Layer 0 is built from dataset A. Adding dataset B:</p>
|
||
<ol>
|
||
<li>For each kmer in B: probe existing layers. If found, the kmer is already indexed.</li>
|
||
<li>Collect kmers of B not present in any layer → set <code>B \ A</code>.</li>
|
||
<li>Build layer 1 from <code>B \ A</code> (dereplicate → count → De Bruijn → unitigs → <code>MphfLayer::build</code>).</li>
|
||
</ol>
|
||
<h3 id="membership-verification">Membership verification</h3>
|
||
<p>ptr_hash maps any input to a valid slot — it does not natively detect absent keys. Membership is verified using the evidence entry: decode the kmer from <code>(chunk_id, rank)</code> and compare to the query. A mismatch means the kmer is absent from this layer; probe the next layer.</p>
|
||
<h3 id="query-algorithm">Query algorithm</h3>
|
||
<div class="highlight"><pre><span></span><code>fn query(kmer) → Option<(layer_index, slot)>:
|
||
for (i, layer) in layers.iter().enumerate():
|
||
slot = layer.mphf.index(kmer)
|
||
if layer.evidence.decode(slot) matches kmer:
|
||
return Some((i, slot))
|
||
return None
|
||
</code></pre></div>
|
||
<p>Expected probe depth: 1 for kmers in layer 0. Each probe is a ptr_hash lookup (~10 ns) plus one evidence decode.</p>
|
||
<h3 id="merging-layers">Merging layers</h3>
|
||
<p>Two layer chains can be merged by re-indexing their union through the full pipeline. This is expensive (full rebuild) but produces an optimal single-layer index. Merge is a maintenance operation, not a query-path requirement.</p>
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