2026-04-16 22:38:20 +02:00
<!doctype html>
< html lang = "en" class = "no-js" >
< head >
< meta charset = "utf-8" >
< meta name = "viewport" content = "width=device-width,initial-scale=1" >
< link rel = "prev" href = "../storage/" >
2026-04-29 22:52:42 +02:00
< link rel = "next" href = "../unitig_evidence/" >
2026-04-16 22:38:20 +02:00
< link rel = "icon" href = "../../assets/images/favicon.png" >
< meta name = "generator" content = "mkdocs-1.6.1, mkdocs-material-9.7.6" >
< title > MPHF selection - obikmer< / title >
< link rel = "stylesheet" href = "../../assets/stylesheets/main.484c7ddc.min.css" >
< link rel = "preconnect" href = "https://fonts.gstatic.com" crossorigin >
< link rel = "stylesheet" href = "https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback" >
< style > : root { --md-text-font : "Roboto" ; --md-code-font : "Roboto Mono" } < / style >
< script > _ _md _scope = new URL ( "../.." , location ) , _ _md _hash = e => [ ... e ] . reduce ( ( ( e , _ ) => ( e << 5 ) - e + _ . charCodeAt ( 0 ) ) , 0 ) , _ _md _get = ( e , _ = localStorage , t = _ _md _scope ) => JSON . parse ( _ . getItem ( t . pathname + "." + e ) ) , _ _md _set = ( e , _ , t = localStorage , a = _ _md _scope ) => { try { t . setItem ( a . pathname + "." + e , JSON . stringify ( _ ) ) } catch ( e ) { } } < / script >
< / head >
< body dir = "ltr" >
< input class = "md-toggle" data-md-toggle = "drawer" type = "checkbox" id = "__drawer" autocomplete = "off" >
< input class = "md-toggle" data-md-toggle = "search" type = "checkbox" id = "__search" autocomplete = "off" >
< label class = "md-overlay" for = "__drawer" > < / label >
< div data-md-component = "skip" >
2026-04-29 22:52:42 +02:00
< a href = "#mphf-selection-two-phase-indexing-architecture" class = "md-skip" >
2026-04-16 22:38:20 +02:00
Skip to content
< / a >
< / div >
< div data-md-component = "announce" >
< / div >
< header class = "md-header md-header--shadow" data-md-component = "header" >
< nav class = "md-header__inner md-grid" aria-label = "Header" >
< a href = "../.." title = "obikmer" class = "md-header__button md-logo" aria-label = "obikmer" data-md-component = "logo" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54" / > < / svg >
< / a >
< label class = "md-header__button md-icon" for = "__drawer" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z" / > < / svg >
< / label >
< div class = "md-header__title" data-md-component = "header-title" >
< div class = "md-header__ellipsis" >
< div class = "md-header__topic" >
< span class = "md-ellipsis" >
obikmer
< / span >
< / div >
< div class = "md-header__topic" data-md-component = "header-topic" >
< span class = "md-ellipsis" >
MPHF selection
< / span >
< / div >
< / div >
< / div >
< script > var palette = _ _md _get ( "__palette" ) ; if ( palette && palette . color ) { if ( "(prefers-color-scheme)" === palette . color . media ) { var media = matchMedia ( "(prefers-color-scheme: light)" ) , input = document . querySelector ( media . matches ? "[data-md-color-media='(prefers-color-scheme: light)']" : "[data-md-color-media='(prefers-color-scheme: dark)']" ) ; palette . color . media = input . getAttribute ( "data-md-color-media" ) , palette . color . scheme = input . getAttribute ( "data-md-color-scheme" ) , palette . color . primary = input . getAttribute ( "data-md-color-primary" ) , palette . color . accent = input . getAttribute ( "data-md-color-accent" ) } for ( var [ key , value ] of Object . entries ( palette . color ) ) document . body . setAttribute ( "data-md-color-" + key , value ) } < / script >
< / nav >
< / header >
< div class = "md-container" data-md-component = "container" >
< main class = "md-main" data-md-component = "main" >
< div class = "md-main__inner md-grid" >
< div class = "md-sidebar md-sidebar--primary" data-md-component = "sidebar" data-md-type = "navigation" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--primary" aria-label = "Navigation" data-md-level = "0" >
< label class = "md-nav__title" for = "__drawer" >
< a href = "../.." title = "obikmer" class = "md-nav__button md-logo" aria-label = "obikmer" data-md-component = "logo" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54" / > < / svg >
< / a >
obikmer
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../.." class = "md-nav__link" >
< span class = "md-ellipsis" >
Home
< / span >
< / a >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
< label class = "md-nav__link" for = "__nav_2" id = "__nav_2_label" tabindex = "0" >
< span class = "md-ellipsis" >
Theory
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_2_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_2" >
< span class = "md-nav__icon md-icon" > < / span >
Theory
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
2026-04-29 22:52:42 +02:00
< a href = "../../kmers/" class = "md-nav__link" >
2026-04-16 22:38:20 +02:00
< span class = "md-ellipsis" >
Kmers and super-kmers
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../theory/encoding/" class = "md-nav__link" >
< span class = "md-ellipsis" >
DNA encoding
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../theory/entropy/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Entropy filter
< / span >
< / a >
< / li >
2026-04-29 22:52:42 +02:00
< li class = "md-nav__item" >
< a href = "../../theory/minimizer/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Minimizer selection
< / span >
< / a >
< / li >
2026-04-16 22:38:20 +02:00
< li class = "md-nav__item" >
< a href = "../../theory/indexing/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Partitioning architecture
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" checked >
< label class = "md-nav__link" for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
< span class = "md-ellipsis" >
Implementation
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_3_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
Implementation
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../superkmer/" class = "md-nav__link" >
< span class = "md-ellipsis" >
SuperKmer
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../kmer/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Kmer
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chunkreader/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Chunk reader
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../pipeline/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Construction pipeline
< / span >
< / a >
< / li >
2026-04-29 22:52:42 +02:00
< li class = "md-nav__item" >
< a href = "../obipipeline/" class = "md-nav__link" >
< span class = "md-ellipsis" >
obipipeline library
< / span >
< / a >
< / li >
2026-04-16 22:38:20 +02:00
< li class = "md-nav__item" >
< a href = "../storage/" class = "md-nav__link" >
< span class = "md-ellipsis" >
On-disk storage
< / span >
< / a >
< / li >
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
< span class = "md-ellipsis" >
MPHF selection
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
< span class = "md-ellipsis" >
MPHF selection
< / span >
< / a >
< nav class = "md-nav md-nav--secondary" aria-label = "Table of contents" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
Table of contents
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
2026-04-29 22:52:42 +02:00
< li class = "md-nav__item" >
< a href = "#indexing-architecture" class = "md-nav__link" >
< span class = "md-ellipsis" >
Indexing architecture
< / span >
< / a >
< nav class = "md-nav" aria-label = "Indexing architecture" >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#superkmer-vs-kmer-counts" class = "md-nav__link" >
< span class = "md-ellipsis" >
Superkmer vs kmer counts
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#phase-1-provisional-index-and-spectrum" class = "md-nav__link" >
< span class = "md-ellipsis" >
Phase 1 — provisional index and spectrum
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#phase-2-definitive-index" class = "md-nav__link" >
< span class = "md-ellipsis" >
Phase 2 — definitive index
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2026-04-16 22:38:20 +02:00
< li class = "md-nav__item" >
< a href = "#candidates" class = "md-nav__link" >
< span class = "md-ellipsis" >
Candidates
< / span >
< / a >
2026-04-29 22:52:42 +02:00
< / li >
< li class = "md-nav__item" >
< a href = "#mphf-choice-per-phase" class = "md-nav__link" >
< span class = "md-ellipsis" >
MPHF choice per phase
< / span >
< / a >
2026-04-16 22:38:20 +02:00
< / li >
< li class = "md-nav__item" >
< a href = "#space-at-scale" class = "md-nav__link" >
< span class = "md-ellipsis" >
Space at scale
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on-disk-and-mmap-considerations" class = "md-nav__link" >
< span class = "md-ellipsis" >
On-disk and mmap considerations
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#open-questions" class = "md-nav__link" >
< span class = "md-ellipsis" >
Open questions
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2026-04-29 22:52:42 +02:00
< li class = "md-nav__item" >
< a href = "../unitig_evidence/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Unitig evidence encoding
< / span >
< / a >
< / li >
2026-04-16 22:38:20 +02:00
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
< span class = "md-ellipsis" >
Architecture
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
Architecture
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../architecture/sequences/invariant/" class = "md-nav__link" >
< span class = "md-ellipsis" >
Sequences
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "Table of contents" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
Table of contents
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
2026-04-29 22:52:42 +02:00
< li class = "md-nav__item" >
< a href = "#indexing-architecture" class = "md-nav__link" >
< span class = "md-ellipsis" >
Indexing architecture
< / span >
< / a >
< nav class = "md-nav" aria-label = "Indexing architecture" >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#superkmer-vs-kmer-counts" class = "md-nav__link" >
< span class = "md-ellipsis" >
Superkmer vs kmer counts
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#phase-1-provisional-index-and-spectrum" class = "md-nav__link" >
< span class = "md-ellipsis" >
Phase 1 — provisional index and spectrum
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#phase-2-definitive-index" class = "md-nav__link" >
< span class = "md-ellipsis" >
Phase 2 — definitive index
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2026-04-16 22:38:20 +02:00
< li class = "md-nav__item" >
< a href = "#candidates" class = "md-nav__link" >
< span class = "md-ellipsis" >
Candidates
< / span >
< / a >
2026-04-29 22:52:42 +02:00
< / li >
< li class = "md-nav__item" >
< a href = "#mphf-choice-per-phase" class = "md-nav__link" >
< span class = "md-ellipsis" >
MPHF choice per phase
< / span >
< / a >
2026-04-16 22:38:20 +02:00
< / li >
< li class = "md-nav__item" >
< a href = "#space-at-scale" class = "md-nav__link" >
< span class = "md-ellipsis" >
Space at scale
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on-disk-and-mmap-considerations" class = "md-nav__link" >
< span class = "md-ellipsis" >
On-disk and mmap considerations
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#open-questions" class = "md-nav__link" >
< span class = "md-ellipsis" >
Open questions
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
2026-04-29 22:52:42 +02:00
< h1 id = "mphf-selection-two-phase-indexing-architecture" > MPHF selection — two-phase indexing architecture< / h1 >
< h2 id = "indexing-architecture" > Indexing architecture< / h2 >
< p > 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.< / p >
< h3 id = "superkmer-vs-kmer-counts" > Superkmer vs kmer counts< / h3 >
< p > The < code > SKFileMeta< / code > sidecar written by < code > SKFileWriter< / code > records < code > instances< / code > (unique superkmers) and < code > length_sum< / code > (total nucleotides). A superkmer of length L contains L − < code > length_sum − × − < / code > . This is an < strong > overestimate< / strong > 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.< / p >
< p > 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.< / p >
< h3 id = "phase-1-provisional-index-and-spectrum" > Phase 1 — provisional index and spectrum< / h3 >
< ol >
< li > Enumerate all kmers from the dereplicated superkmers of the partition.< / li >
< li > Build a provisional MPHF over this key set; capacity is pre-allocated from the sidecar estimate (slight overestimate, harmless).< / li >
< li > Accumulate counts: for each kmer in each superkmer, < code > count[MPHF(kmer)] += sk.count()< / code > .< / li >
< li > Compute the kmer frequency spectrum (histogram: occurrences → number of kmers).< / li >
< li > Apply count filter (e.g. discard singletons). After filtering, the exact number of surviving kmers is known.< / li >
< li > Discard the provisional MPHF.< / li >
< / ol >
< h3 id = "phase-2-definitive-index" > Phase 2 — definitive index< / h3 >
< p > 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).< / p >
< hr / >
2026-04-16 22:38:20 +02:00
< h2 id = "candidates" > 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 > Parallel construction; well-tested with DNA kmer data at scale< / li >
2026-04-29 22:52:42 +02:00
< li > Drawback: largest space footprint; streaming construction (no exact count needed) was its main differentiator — irrelevant here since exact count is available at phase 2< / li >
2026-04-16 22:38:20 +02:00
< / ul >
< p > < strong > ptr_hash< / strong > (PtrHash algorithm, Groot Koerkamp, SEA 2025):< / p >
< ul >
< li > ~2.4 bits/key; fastest queries (≥2.1× – × < / li >
2026-04-29 22:52:42 +02:00
< li > Requires exact key count at construction — available at phase 2< / li >
2026-04-16 22:38:20 +02:00
< li > Drawback: published February 2025 — very young, no production track record< / li >
< / ul >
< p > < strong > FMPHGO< / strong > (< code > ph< / code > crate, Beling, ACM JEA 2023):< / p >
< ul >
< li > ~2.1 bits/key — most compact of the three; good query speed; parallelisable construction< / li >
< li > More established than ptr_hash; actively maintained< / li >
2026-04-29 22:52:42 +02:00
< li > Works well with overestimated capacity → natural fit for phase 1< / li >
2026-04-16 22:38:20 +02:00
< / ul >
2026-04-29 22:52:42 +02:00
< h2 id = "mphf-choice-per-phase" > MPHF choice per phase< / h2 >
< p > < strong > Phase 1< / strong > (provisional, discarded after spectrum computation): FMPHGO. Tolerates overestimated capacity, compact, no need to optimise for query speed on a temporary structure.< / p >
< p > < strong > Phase 2< / strong > (persistent, queried repeatedly): open between FMPHGO and ptr_hash. Exact key count is available, so both operate optimally. ptr_hash's query speed advantage (2.1– × < / p >
< p > boomphf is effectively eliminated: its space overhead is the largest and its streaming-construction advantage does not apply here.< / p >
< hr / >
2026-04-16 22:38:20 +02:00
< h2 id = "space-at-scale" > Space at scale< / h2 >
2026-04-29 22:52:42 +02:00
< p > For 1 024 partitions × < / p >
2026-04-16 22:38:20 +02:00
< 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 > FMPHGO< / td >
< td > 2.1< / td >
< td > ~27 GB< / td >
< / tr >
< / tbody >
< / table >
2026-04-29 22:52:42 +02:00
< p > For a human genome at 30× – – < / p >
2026-04-16 22:38:20 +02:00
< h2 id = "on-disk-and-mmap-considerations" > On-disk and mmap considerations< / h2 >
< p > 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 < code > ph< / code > crate currently uses serde, so loading involves a copy. Given per-partition MPHF sizes of 1– < / p >
< p > No established Rust crate provides a natively on-disk MPHF. < strong > SSHash< / strong > (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.< / p >
< h2 id = "open-questions" > Open questions< / h2 >
< ul >
2026-04-29 22:52:42 +02:00
< li > Confirm actual partition sizes and overestimation factor on representative metagenomic datasets.< / li >
< li > Revisit ptr_hash for phase 2 once the crate has broader production track record.< / li >
< li > Assess rkyv integration cost for FMPHGO if true zero-copy mmap becomes necessary for the persistent index.< / li >
2026-04-16 22:38:20 +02:00
< li > Keep SSHash in mind if the indexing architecture is reconsidered at a higher level.< / li >
< / ul >
< / article >
< / div >
< script > var target = document . getElementById ( location . hash . slice ( 1 ) ) ; target && target . name && ( target . checked = target . name . startsWith ( "__tabbed_" ) ) < / script >
< / div >
< / main >
< footer class = "md-footer" >
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
Made with
< a href = "https://squidfunk.github.io/mkdocs-material/" target = "_blank" rel = "noopener" >
Material for MkDocs
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
< script id = "__config" type = "application/json" > { "annotate" : null , "base" : "../.." , "features" : [ ] , "search" : "../../assets/javascripts/workers/search.2c215733.min.js" , "tags" : null , "translations" : { "clipboard.copied" : "Copied to clipboard" , "clipboard.copy" : "Copy to clipboard" , "search.result.more.one" : "1 more on this page" , "search.result.more.other" : "# more on this page" , "search.result.none" : "No matching documents" , "search.result.one" : "1 matching document" , "search.result.other" : "# matching documents" , "search.result.placeholder" : "Type to start searching" , "search.result.term.missing" : "Missing" , "select.version" : "Select version" } , "version" : null } < / script >
< script src = "../../assets/javascripts/bundle.79ae519e.min.js" > < / script >
< script src = "https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js" > < / script >
< / body >
< / html >
