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).
- Drawback: largest space footprint; streaming construction (no exact count needed) was its main differentiator — irrelevant here since exact count is available at phase 2
- 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.
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.
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.
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.
- **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.
