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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 − </ 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 − </ 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" FPVF" (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" > & </ 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" > -> </ 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" > & </ 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" > & </ 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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