obikmer/docmd/implementation/mphf.md

MPHF selection — two-phase indexing architecture

Indexing architecture

Kmer indexing per partition proceeds in two phases. The separation is necessary because the exact number of unique kmers in a partition is not known until after counting and filtering.

Superkmer vs kmer counts

The SKFileMeta sidecar written by SKFileWriter records instances (unique superkmers) and length_sum (total nucleotides). A superkmer of length L contains L − k + 1 kmers, so the kmer count per partition can be estimated as length_sum − instances × (k − 1). This is an overestimate of unique kmers: two distinct superkmers (different flanking contexts, same minimizer) can share kmers. The exact count of unique kmers is only known after enumerating and deduplicating them.

Note: two superkmers sharing a kmer necessarily share the same minimizer and therefore always land in the same partition — no kmer can appear in two different partitions.

Phase 1 — provisional index and spectrum

1. Enumerate all kmers from the dereplicated superkmers of the partition.
2. Build a provisional MPHF over this key set; capacity is pre-allocated from the sidecar estimate (slight overestimate, harmless).
3. Accumulate counts: for each kmer in each superkmer, count[MPHF(kmer)] += sk.count().
4. Compute the kmer frequency spectrum (histogram: occurrences → number of kmers).
5. Apply count filter (e.g. discard singletons). After filtering, the exact number of surviving kmers is known.
6. Discard the provisional MPHF.

Phase 2 — definitive index

Build a new MPHF over the filtered kmer set only, with the exact key count available. This is the persistent per-partition index used for all downstream operations (queries, set operations).

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Candidates

boomphf (BBHash algorithm, maintained by 10X Genomics):

• ~3.7 bits/key; mature crate, used in production bioinformatics (Pufferfish, Piscem)
• Parallel construction; well-tested with DNA kmer data at scale
• Drawback: largest space footprint; streaming construction (no exact count needed) was its main differentiator — irrelevant here since exact count is available at phase 2

ptr_hash (PtrHash algorithm, Groot Koerkamp, SEA 2025):

• ~2.4 bits/key; fastest queries (≥2.1× over alternatives, 8–12 ns/key for u64 in tight loops) and fastest construction (≥3.1×)
• Requires exact key count at construction — available at phase 2
• Drawback: published February 2025 — very young, no production track record

FMPHGO (ph crate, Beling, ACM JEA 2023):

• ~2.1 bits/key — most compact of the three; good query speed; parallelisable construction
• More established than ptr_hash; actively maintained
• Works well with overestimated capacity → natural fit for phase 1

MPHF choice per phase

Phase 1 (provisional, discarded after spectrum computation): FMPHGO. Tolerates overestimated capacity, compact, no need to optimise for query speed on a temporary structure.

Phase 2 (persistent, queried repeatedly): ptr_hash. Exact key count is available at phase 2, so ptr_hash operates optimally. Its query speed (≥2.1× over FMPHGO) and construction speed (≥3.1×) are meaningful for the persistent index; the space overhead at 2.4 bits/key is acceptable. The crate's youth (Feb 2025) was previously a concern; it is now accepted given the performance profile and the fact that each layer MPHF is independently rebuildable from its unitig file if needed.

boomphf is effectively eliminated: its space overhead is the largest and its streaming-construction advantage does not apply here.

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Space at scale

For 1 024 partitions × 100 M kmers/partition (phase 2 index, after filtering):

MPHF	bits/key	Total MPHF size
boomphf	3.7	~47 GB
ptr_hash	2.4	~31 GB
FMPHGO	2.1	~27 GB

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.

On-disk and mmap considerations

All three are in-memory structures. Their internal representation is flat bit arrays (no heap pointers), making them serialisable as contiguous byte blobs and mmappable per partition. True zero-copy access would require rkyv integration; the ph crate currently uses serde, so loading involves a copy. Given per-partition MPHF sizes of 1–8 MB, the OS page cache handles this transparently — strict zero-copy is a refinement, not a blocker.

No established Rust crate provides a natively on-disk MPHF. SSHash (Sparse and Skew Hash) is a complete kmer dictionary designed for disk access and is order-preserving (overlapping kmers receive consecutive indices → cache-friendly count access), but it is C++-only and covers more than just the MPHF layer.

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Multilayer index architecture

Motivation

An index built from a single dataset A can be extended with a new dataset B without rebuilding. This supports incremental construction (adding species, samples, or sequencing runs) and enables set operations across heterogeneous sources.

Layer structure

Each layer is a self-contained unit:

layer_i/
  unitigs.bin     — packed 2-bit nucleotide sequences
  mphf.bin        — ptr_hash index (phase-2, exact key count)
  evidence.bin    — [(unitig_id, rank)] per MPHF slot  (see unitig_evidence.md)
  counts.bin      — [u32] per MPHF slot

Layers are disjoint: a canonical kmer belongs to exactly one layer. Layer 0 is built from dataset A. Adding dataset B proceeds as follows:

1. For each kmer in B: query layer 0 — if found, accumulate count into counts_0[MPHF_0(kmer)].
2. Collect all kmers of B not present in any existing layer → set B \ A.
3. Build layer 1 from B \ A using the standard two-phase pipeline (spectrum, filter, ptr_hash).

Adding a third dataset C repeats the process: probe layer 0, then layer 1, then build layer 2 from C \ A \ B.

Membership verification

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 (unitig_id, rank) and compare to the query. A mismatch means the kmer is absent from this layer; probe the next layer.

This makes the evidence layer load-bearing for correctness, not only for locality.

Query algorithm

fn query(kmer) → Option<count>:
    for layer in layers:
        slot = layer.mphf.query(kmer)
        if layer.evidence.decode(slot) == kmer:
            return Some(layer.counts[slot])
    return None

Expected probe depth: 1 for kmers present in layer 0, increasing for rare kmers added in later layers. In practice, the dominant dataset (largest A) should be layer 0 to minimise average probe depth.

Layer count and probe cost

Each probe is a ptr_hash lookup (~10 ns) plus one evidence decode (two array accesses). For L layers the worst case is L probes + 1 None. In practice L is small (2–5 for typical multi-species databases). No global data structure is needed to route queries; the layer chain is traversed in order.

Merging layers

Two layer chains can be merged by re-indexing their union through the standard pipeline. This is expensive (full rebuild) but produces an optimal single-layer index. Merge is a maintenance operation, not a query-path requirement.

Open questions

• Confirm actual partition sizes and overestimation factor on representative metagenomic datasets.
• rkyv integration: all flat arrays in a layer (evidence, counts, presence/absence matrix) map trivially to rkyv::Archive — fixed-size element types, no heap indirection. The presence/absence matrix is the strongest case: at 10 M kmers × 1 000 samples ≈ 1.25 GB per partition, zero-copy mmap via rkyv avoids loading the entire matrix at open time, letting the OS page cache serve only accessed pages. ptr_hash itself is internally a flat bit array and is structurally compatible with rkyv, but requires either native crate support or a wrapper. Assess the wrapper cost and whether ptr_hash is willing to adopt rkyv upstream.
• Keep SSHash in mind if the indexing architecture is reconsidered at a higher level.
• Determine optimal layer ordering heuristic (by kmer count? by query frequency?) for multi-species databases.