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MPHF selection
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MPHF selection
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Why two phases are needed
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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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Space at scale
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ptr_hash configuration (phase 2)
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Multilayer index architecture
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Layer structure
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Evidence modes
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Membership verification
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Query algorithm
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Merging layers
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Unitig evidence encoding
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Evidence elimination (discussion)
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obilayeredmap crate
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PersistentCompactIntVec
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PersistentBitVec
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Merge command
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Kmer filtering (rebuild/dump/unitig)
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Architecture
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Sequences
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Why two phases are needed
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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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Space at scale
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ptr_hash configuration (phase 2)
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Multilayer index architecture
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Layer structure
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Evidence modes
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Build functions
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Membership verification
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Query algorithm
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Merging layers
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< h1 id = "mphf-selection-two-phase-indexing-architecture" > MPHF selection — two-phase indexing architecture</ h1 >
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< 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 >
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< p > Implemented in < code > obikpartitionner::KmerPartition::count_kmer()</ code > → < code > count_partition()</ code > .</ p >
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< ol >
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< li >< strong > External sort</ strong > : read the dereplicated superkmer file; extract the raw < code > u64</ code > canonical kmer value for every kmer of every superkmer. Sort in RAM-bounded chunks (adaptive budget: 40% of available RAM ÷ n_threads, minimum 1 M kmers per chunk), then k-way merge with inline dedup. Result: < code > sorted_unique.bin</ code > — a flat array of f0 distinct sorted < code > u64</ code > values. Exact kmer count f0 is known at this point.</ li >
< li >< strong > Build provisional MPHF</ strong > (ptr_hash, same configuration as phase 2) over < code > sorted_unique.bin</ code > using < code > new_from_par_iter</ code > . Delete < code > sorted_unique.bin</ code > immediately after. Persist to < code > mphf1.bin</ code > .</ li >
< li >< strong > Create < code > counts1.bin</ code ></ strong > : < code > PersistentCompactIntVec</ code > with f0 slots, zero-initialised.</ li >
< li >< strong > Accumulation pass</ strong > : re-read the dereplicated superkmer file; for each kmer in each superkmer, compute < code > slot = mphf.index(kmer.raw())</ code > and increment < code > counts1[slot]</ code > by the superkmer's COUNT.</ li >
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< 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/
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mphf1.bin — ptr_hash provisional MPHF (discarded after phase 2)
counts1.bin — PersistentCompactIntVec, f0 ×
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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 >
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< p >< code > MphfLayer::build(dir, block_bits, mode: & IndexMode, fill_slot)</ code > is called on the unitig directory:</ p >
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< ol >
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< li >< strong > Pass 1</ strong > (parallel): a < code > CanonicalKmerIter</ code > — clonable via < code > Arc< Mmap> </ code > , no file reopening — is passed directly to < code > new_from_par_iter</ code > via < code > par_bridge()</ code > . No < code > .idx</ code > is read or created at this stage; parallelism is at partition/layer level, not within a single MPHF. Produces < code > mphf.bin</ code > .</ li >
< li >< strong > Pass 2</ strong > (sequential): iterate with < code > iter_indexed_canonical_kmers</ code > ; fill evidence files; call < code > fill_slot(slot, kmer)</ code > callback per kmer. For Exact/Hybrid, < code > .idx</ code > is written at the end of this pass — never earlier.</ li >
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</ ol >
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< p >< code > mphf1.bin</ code > and < code > counts1.bin</ code > are no longer needed after phase 2 and can be deleted.</ p >
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< hr />
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< h2 id = "mphf-candidates" > MPHF candidates</ h2 >
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< 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 >
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< 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 >
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</ ul >
< p >< strong > ptr_hash</ strong > (PtrHash algorithm, Groot Koerkamp, SEA 2025):</ p >
< ul >
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< li > ~2.4 bits/key; fastest queries (≥2.1× – × </ 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 >
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</ ul >
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< p >< strong > FMPH/FMPHGO</ strong > (< code > ph</ code > crate, Beling, ACM JEA 2023):</ p >
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< ul >
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< li > ~2.1 bits/key — most compact; good query speed; deterministic construction</ li >
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< li >< code > GOFunction</ code > (group-oriented variant) was the original phase-1 choice; eliminated when the external sort made the exact count available at phase 1 as well</ li >
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</ ul >
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< h2 id = "mphf-choice-per-phase" > MPHF choice per phase</ h2 >
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< p >< strong > Both phases</ strong > : < strong > ptr_hash</ strong > , same type alias and construction parameters. The external sort (phase 1) and the unitig index (phase 2) both provide the exact key count before MPHF construction, so ptr_hash's requirement is satisfied in both cases. Using a single MPHF implementation removes the < code > ph</ code > crate dependency.</ p >
< p > boomphf: eliminated — largest space overhead, streaming advantage no longer needed. FMPH/GOFunction: eliminated — exact count available, ptr_hash is faster at equivalent compactness.</ p >
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< hr />
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< h2 id = "space-at-scale" > Space at scale</ h2 >
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< p > For 1 024 partitions × </ p >
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< 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 >
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< td > FMPH</ td >
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< td > 2.1</ td >
< td > ~27 GB</ td >
</ tr >
</ tbody >
</ table >
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< p > For a human genome at 30× – – </ p >
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< 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 </ 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 × < code > Linear/λ=3.0</ code > , 20% less space. < code > default_compact</ code > (λ=4.0) saves a further 12.5% at 2× </ 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 >
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< hr />
< h2 id = "multilayer-index-architecture" > Multilayer index architecture</ h2 >
< h3 id = "layer-structure" > Layer structure</ h3 >
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< 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 >
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< div class = "highlight" >< pre >< span ></ span >< code > layer_i/
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unitigs.bin — packed 2-bit nucleotide sequences (kmer evidence source)
unitigs.bin.idx — random-access block index (block_bits controls granularity)
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mphf.bin — ptr_hash phase-2 MPHF
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evidence.bin — n ×
fingerprint.bin — n ×
[no layer_meta.json — mode stored once in partition-level meta.json]
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</ code ></ pre ></ div >
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< 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 >
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< ol >
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< 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 >
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</ ol >
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< h3 id = "evidence-modes" > Evidence modes</ h3 >
< p > Three evidence modes are supported via < code > IndexMode</ code > , stored once in < code > PartitionMeta</ code > at partition root. There is no < code > layer_meta.json</ code > .</ p >
< p >< strong > Exact</ strong > (< code > IndexMode::Exact</ code > ): < code > evidence.bin</ code > stores one < code > (chunk_id, rank)</ code > pair per MPHF slot. Verification reconstructs the kmer and compares to the query. Zero false positives. < code > .idx</ code > required at query time.</ p >
< p >< strong > Approx</ strong > (< code > IndexMode::Approx { b, z }</ code > ): < code > fingerprint.bin</ code > stores a b-bit hash per slot. False-positive rate 1/2^b per query; Findere z-parameter reduces window FP to ≈ 1/2^(b·z). No < code > .idx</ code > written or needed.</ p >
< p >< strong > Hybrid</ strong > (< code > IndexMode::Hybrid { b, z }</ code > ): both < code > fingerprint.bin</ code > and < code > evidence.bin</ code > + < code > .idx</ code > . < code > find()</ code > uses the fingerprint (O(1)); < code > find_strict()</ code > uses exact evidence (O(1)).</ p >
< h3 id = "build-functions" > Build functions</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code > MphfLayer::build(dir, block_bits, mode: & IndexMode, fill_slot)
Pass 1: CanonicalKmerIter + par_bridge() → build mphf.bin (no .idx used)
Pass 2: sequential iter → fill evidence files + call fill_slot
.idx written last for Exact/Hybrid (query-time only)
MphfLayer::build_exact_evidence(dir, block_bits)
Post-hoc: builds evidence.bin + .idx from existing mphf.bin + unitigs.bin
Uses open_sequential(); no .idx required on entry
MphfLayer::build_approx_evidence(dir, b, z)
Post-hoc: builds fingerprint.bin from existing mphf.bin + unitigs.bin
Uses open_sequential(); never writes .idx
</ code ></ pre ></ div >
< p > There is no < code > build_evidence</ code > dispatch wrapper. Callers choose the appropriate post-hoc build directly.</ p >
< p > In < code > obikpartitionner</ code > , < code > build_index_layer</ code > receives < code > block_bits: u8</ code > from < code > IndexConfig::block_bits</ code > and forwards it directly to < code > Layer::build</ code > and < code > Layer::build_approx_evidence</ code > .</ p >
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< h3 id = "membership-verification" > Membership verification</ h3 >
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< p > ptr_hash maps any input to a valid slot — it does not natively detect absent keys. Membership is verified using the evidence entry:</ p >
< ul >
< li >< strong > Exact</ strong > : decode < code > (chunk_id, rank)</ code > from < code > evidence.bin</ code > ; reconstruct the kmer via < code > unitigs.verify_canonical_kmer</ code > ; compare to query.</ li >
< li >< strong > Approx</ strong > : compare < code > kmer.seq_hash()</ code > to the b-bit fingerprint stored at the slot.</ li >
</ ul >
< p > A mismatch in either mode means the kmer is absent from this layer; probe the next layer.</ p >
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< h3 id = "query-algorithm" > Query algorithm</ h3 >
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< 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)
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if layer.evidence.matches(slot, kmer): // exact or approx dispatch
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return Some((i, slot))
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return None
</ code ></ pre ></ div >
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< p >< code > MphfLayer::find</ code > dispatches on < code > LayerEvidence</ code > at O(1) — no panicking < code > find_exact</ code > /< code > find_approx</ code > methods. < code > find_strict</ code > always performs an exact check: O(1) for Exact/Hybrid, O(n) sequential scan for Approx. Expected probe depth: 1 for kmers in layer 0. Each probe is a ptr_hash lookup (~10 ns) plus one evidence check.</ p >
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< h3 id = "merging-layers" > Merging layers</ h3 >
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< 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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