lexindex

Compact, immutable string ↔ id indexes for huge catalogs, with a Rust core and Python bindings. Build once over a set of strings — entity names, document keys, vocabulary terms, cluster labels — persist a flat blob, and query it many times, memory-mapped where the structure allows. Pairs with betula-cluster (string ids ↔ cluster ids, both ways) but stands on its own.

Five indexes

• StringIndex — an ordered index that is the finite-state transducer (fst) alone: exact string ↔ id, prefix, common prefix (the keys a query starts with, in one walk), range, predecessor / successor, fuzzy (bounded Levenshtein distance), subsequence and lazy in-order iteration, all automata over the FST with no key list to scan. Autocomplete, fuzzy search, ordered browse.
• DictIndex — an ordered dictionary with the key stored for every id: string ↔ rank both ways, lower_bound, prefix, common_prefix, range, in-order iteration — no automata, so no fuzzy. The sorted keys front-coded in blocks of 256, each cut into microblocks of 32, the suffixes under a symbol table trained on the 65 536 keys around them: 2.84 bytes/key, 52 % below StringIndex, id 298–302 ns against its 265–272, key_into 207 against its key at 466–473. A prefix is a range here, not an automaton walk, so prefix_count is two order lookups — 375 ns where marisa-trie must enumerate every match to count it (123 444). Blocks of 512 store 2.81 bytes/key, under marisa-trie at every setting it has on this corpus — over the thirteen-corpus set the ranking goes both ways, marisa smaller wherever the keys share deep structure and DictIndex smaller where they do not, while DictIndex answers faster on all but numeric, 1.8–2.9× at a million keys. Exact queries, every id back to its key, small.
• CompactHashIndex — the smallest string → dense id map: an in-crate minimal perfect hash plus a fingerprint per key, no keys stored. 1.26 bytes/key on real words — 2.4× below marisa-trie — and 0.76 at a 4-bit fingerprint (6.25 % false positives), for probabilistic membership (about 2^-bits) and no reverse lookup. Footprint first, a rare false positive acceptable.
• ClosedHashIndex — the perfect hash and nothing else: id(key) -> u32, no Option — a member's id, and some id in [0, n) for anything else. 0.26 bytes/key, a fifth of CompactHashIndex, and a lookup at id_unchecked's cost (40 ns on the dictionary, against 68 for the fingerprint-checked id). A token → id map where every query is a member by construction.
• PerfectHashIndex — the perfect hash with the keys stored: verified membership and id → key, no ordering. id_unchecked skips the compare and runs 4.1× as fast as std::HashMap; fingerprints=True adds one byte per key so an absent key stops after one cache miss instead of two (166 → 74 ns on the dictionary) — a stop list, a block list. A fixed-vocabulary token ↔ id map on a hot path.

All five assign dense ids in [0, n), build deterministically and serialise to a flat blob: save / load everywhere, zero-copy load_mmap where there is more than the perfect hash to map. They are immutable; Overlay adds and removes keys on StringIndex, CompactHashIndex and PerfectHashIndex without a rebuild, keeps every id stable, and folds the edits into a fresh base with compact(). The other two are absent by design rather than omission: an overlay issues a new key the next id after the base, which is exactly what DictIndex cannot accept — its ids are the lexicographic rank, and a key added in the middle of the order would not get one — and ClosedHashIndex has no membership to ask, so there is no "already in the base" for an overlay to test against. Every configuration builds on 32-bit targets, wasm32-unknown-unknown included (leave mmap off there — nothing to map).

Install

pip install lexindex      # one abi3 wheel for CPython 3.11+, no runtime dependencies

[dependencies]
lexindex = "3.0"
# fst-only (drop the memory-mapping and perfect-hash code):
# lexindex = { version = "3.0", default-features = false }

Python

from lexindex import ClosedHashIndex, CompactHashIndex, DictIndex, PerfectHashIndex, StringIndex

idx = StringIndex(["apple", "apricot", "banana", "cherry"])
idx.id("banana")             # 2  (sorted rank)
idx.key(0)                   # "apple"  — reconstructed from the FST, no stored reverse map
idx.prefix("ap")             # [("apple", 0), ("apricot", 1)]
idx.fuzzy("aple", 1)         # [("apple", 0)]  — typo-tolerant
idx.successor("ba")          # ("banana", 2)   — nearest key >= query
idx.ids_of(["apple", "x"])   # [0, None]  — batched: one FFI call, not one per key
idx.save("catalog.bix")      # StringIndex.load("catalog.bix") reloads it; load_mmap borrows it zero-copy

c = CompactHashIndex(["GET", "POST", "PUT", "DELETE"])  # ~1.3 B/key at scale; fingerprint_bits=4 → ~0.8
c.id("POST")                 # dense id in [0, n); probabilistic membership, no id → key
c.id_unchecked("POST")       # fastest lookup for a known-closed vocabulary

z = ClosedHashIndex(["GET", "POST", "PUT", "DELETE"])   # the perfect hash alone, ~0.26 B/key
z.id("POST")                 # a member's id; any other string gets *some* id in [0, n)

w = DictIndex(["GET", "POST", "PUT", "DELETE"])         # ordered, keys stored, ~2.84 B/key
w.id("POST")                 # 2  (sorted rank); w.key(2) == "POST"; w.lower_bound("P") == 2

d = PerfectHashIndex(["GET", "POST", "PUT", "DELETE"])  # verified membership and id → key
d.key(d.id("POST"))          # "POST"; d.id("PATCH") is None

examples/quickstart.py runs all five end to end; the usage guide covers every interface, including batched lookups into NumPy and Arrow buffers and free-threaded CPython.

With betula-cluster: the lexindex dense id is the embedding-matrix row, so string id → cluster and cluster → string ids are both one lookup (runnable):

idx = PerfectHashIndex(doc_ids)                  # string id <-> dense [0, n) id
matrix[idx.id(doc_id)] = embedding[doc_id]       # row index == lexindex id
labels = betula_cluster.fit_predict(matrix, n_clusters=k)
cluster = labels[idx.id("doc-00042")]            # string id -> cluster
members = [idx.key(int(r)) for r in (labels == cluster).nonzero()[0]]  # cluster -> string ids

Rust

use lexindex::StringIndex;

let idx = StringIndex::build(["apple", "apricot", "banana", "cherry"])?;
assert_eq!(idx.id("banana"), Some(2));                  // string → id (sorted rank)
assert_eq!(idx.key(0).as_deref(), Some("apple"));       // id → string, a rank-walk over the FST

// prefix / range / fuzzy / subsequence, all lexicographically ordered
let fruit: Vec<_> = idx.prefix("ap").into_iter().map(|(k, _)| k).collect();
assert_eq!(fruit, ["apple", "apricot"]);
let near: Vec<_> = idx.fuzzy("aple", 1)?.into_iter().map(|(k, _)| k).collect();
assert_eq!(near, ["apple"]);                            // Levenshtein distance ≤ 1
let sub: Vec<_> = idx.subsequence("ap").into_iter().map(|(k, _)| k).collect();
assert_eq!(sub, ["apple", "apricot"]);

// a flat blob: reload it, or borrow it zero-copy from the file
idx.save("catalog.bix")?;
// SAFETY: nothing may modify the file while a mapped index borrows it (see `load_mmap`).
let idx = unsafe { StringIndex::load_mmap("catalog.bix") }?; // no read into RAM; pages shared
# drop(idx);
# std::fs::remove_file("catalog.bix").ok();
# Ok::<(), lexindex::IndexError>(())

use lexindex::{ClosedHashIndex, CompactHashIndex, DictIndex, PerfectHashIndex};

let verbs = ["GET", "POST", "PUT", "DELETE"];

// The smallest string → id map: an 8-bit fingerprint per key, ~1.3 B/key, ~0.4 % false positives.
let compact = CompactHashIndex::build(verbs, 1)?;
let id = compact.id("POST").unwrap();                  // Some(slot); a stranger may rarely read as present
assert_eq!(compact.id_unchecked("POST"), id);          // no fingerprint check, for a closed vocabulary

// The perfect hash alone, ~0.26 B/key: a member's id, and *some* id in [0, n) for anything else.
let closed = ClosedHashIndex::build(verbs)?;
assert!((closed.id("POST") as usize) < closed.len());

// Verified membership and id → key, the keys stored; ids survive save / load on every index.
let exact = PerfectHashIndex::build(verbs)?;
let id = exact.id("POST").unwrap();
assert_eq!(exact.key(id), Some("POST"));
assert_eq!(exact.id("PATCH"), None);
exact.save("verbs.bmp")?;
assert_eq!(PerfectHashIndex::load("verbs.bmp")?.id("POST"), Some(id));

// Ordered, the key stored for every id, ~3.2 B/key; prefix and range, no fuzzy.
let dict = DictIndex::build(verbs)?;
assert_eq!(dict.id("POST"), Some(2));                  // the sorted rank
assert_eq!(dict.key(2).as_deref(), Some("POST"));
assert_eq!(dict.lower_bound("P"), 2);                  // the "P…" keys are ids 2..lower_bound("Q")
# std::fs::remove_file("verbs.bmp").ok();
# Ok::<(), lexindex::IndexError>(())

Design notes

One line each; the sections are in the design notes.

• StringIndex is the FST alone. id → key is a rank-walk over the automaton, so the blob is [magic "BIX4"][fst] and there is no reverse map to store or keep in sync.
• DictIndex is front coding under a symbol table. Blocks of 256 sorted keys, the first whole, cut into microblocks of 32 whose first keys are coded against each other and the rest against their predecessors as (shared-prefix length, suffix) — one byte a header, the headers of a run before its suffixes — the suffixes under a 255-symbol FSST-style table (its own format) trained on the index's own suffixes; a lookup walks the microblock heads to one microblock, rules most of its entries out by the header alone and compares the rest against the probe without decoding them.
• CompactHashIndex stores no keys. A minimal perfect hash plus one fingerprint_bits-wide fingerprint per slot from a second, uncorrelated hash — a design rate of about 2^-bits, not a defence against chosen queries. Its build streams 16 bytes per key, never the strings: 302 MB peak at 100 M keys against 8.8 GB for a list, 0.94 GB at 10⁹.
• ClosedHashIndex is that perfect hash alone — the same slot CompactHashIndex::id_unchecked gives, with a signature that says nothing can tell a member from a stranger.
• PerfectHashIndex verifies every hit against the stored key. The pair in a billion that collides in the 64-bit hash is served, still exactly, from a side table the hot path never reads.
• Keys are bytes. No Unicode normalisation, case folding or collation: normalise (NFC/NFKC, casefold) before building and before querying if the application needs it.
• Every build is deterministic. The same keys give the same blob, byte for byte, on any machine and thread count — within one version; ids are arbitrary and change whenever the key set does, so persist the blob rather than re-derive it.
• Loading is safe; mapping is unsafe. from_bytes and load take arbitrary bytes on every index — the reason the perfect hash is in-crate — and a crafted blob answers wrong ids, never out-of-range ones. load_mmap and its _verified / _untrusted forms borrow the mapped pages, so the file must not change while the index is alive.
• Blobs move forward, not backward. 2.0 replaced the key hash (the previous one had a two-word collision family on ordinary text), so every hash blob written before it (BMP5, BMP6, BCH6) is refused by name and rebuilt from the keys; BIX4 crosses the versions unchanged, and an OVL2 does when its base is one — an overlay embeds its base, so one over a 1.x hash blob is refused with it.
• --no-default-features is fst only (StringIndex, DictIndex, Overlay); mph adds no dependency, so the whole tree is fst plus memmap2, and cargo audit reports nothing on either.

Benchmarks

Serialised size on real English words

python bench/compare.py on /usr/share/dict/words (479 823 words, 9.3 B/key raw). Keys are a real vocabulary, never a synthetic entity-{i} sequence — sequential keys collapse the FST to a near-regular automaton and report a misleading ~0 B/key, so the benchmark refuses them. Smaller is better; the capability columns are why you would still pick a larger one.

_{Generated by bench/compare.py — raw numbers and the machine that produced them: bench/results/compare-2026-09-12-arz-386b2e6.json — every cell's build and lookup samples, the false-positive measurement, the CPU, kernel, rustc, Python and the load average at both ends of the run. ns/lookup is one exact lookup through Python over 100 000 probes, half of them plausible near-misses, shuffled — the counterweight to the size column, since bytes alone read as though the smallest structure were the best one. Every row pays a 48 ns call boundary, which is what the empty loop and call cost in this run, against 49 in the run the table published through 2.1.0 came from; bench/reproduce.sh prints the two side by side because that floor has measured 100 in another session, and a column from such a run is only comparable within itself. The builtin dict is in the table because it is the thing being replaced. The four smallest rows are also the fastest, and for the same reason: they store no keys, so a miss is only probably detected and there is no id → key on offer. The two DictIndex rows are one type at two block sizes; it builds in 136–137 ms against marisa-trie's 237–240, and the larger block trades reverse-lookup latency for the bytes. marisa-trie appears three times for the same reason it has tuning parameters: its own documentation says the right setting depends on the data, so the table carries its compact end, its default and its fast end rather than one point somebody could fairly call untuned. The benchmark notes table the whole block-size curve, the prefix queries, and the same nine structures over a pinned set of thirteen corpora at three scales — where the ranking between DictIndex and marisa-trie reverses with how much the keys share, which one word list cannot show.}

Two claims, scoped to libraries a Python or Rust project can install — research-grade C++ tries (CoCo-trie, C², XCDAT, PDT, SuRF) are the published frontier and are cited, not claimed against, since none has a binding to benchmark here. CompactHashIndex is the smallest string → dense id map here, 2.4× below marisa-trie at the default 8-bit fingerprint and 3.9× at 4 bits, when a bounded false-positive rate is acceptable: about 2^-fingerprint_bits by design, measured 6.2530 % at 4 bits and 1.5553 % at 6 over 2 M non-member probes (z = +0.18 / −0.83 against theory), ≈0.4 % at 8, ≈0.0015 % at 16. Both hashes are deterministic and unseeded, so an adversary who chooses the queries can find false positives at will — it is not a security primitive. StringIndex is the only structure here that answers fuzzy and subsequence queries, at 4× below a plain DAWG; ordered range queries DictIndex answers too, and more cheaply. On this corpus DictIndex at its default block is smaller than marisa-trie while answering everything marisa does and key(id), lower_bound and range besides — but a trie's size swings 3× across corpora and marisa has tuning parameters of its own, so that is a result about these words at these settings rather than a general ranking (how it was measured).

Which one to pick

Every size above is one corpus at one n, and the ranking is stable across neither: a trie's size depends on how much the keys share, a fingerprint index's does not (three corpora, and 10 M). plan does this on your keys. lexindex.plan(keys, prefix=True) in Python, lexindex::plan(&keys, Needs::default().prefix()) in Rust: it prices every index that answers what you asked for, ranks them cheapest first, and says when two are too close to call or when the corpus is one its model cannot carry. Past 100 000 keys it models from a sample of that size and lands within 1.4 % of the built DictIndex blob at the median, 5.1 % at worst; below it, it builds the candidates and reports what they weigh. By hand, in decision order:

• Do the keys need to come back out, or be scanned in order? Then the fingerprint indexes are out: StringIndex for prefix / range / fuzzy, DictIndex for exact string ↔ rank at 52 % less, PerfectHashIndex for id → key without ordering — and each pays for the keys it stores.
• Is a bounded false-positive rate acceptable? Then CompactHashIndex: 2.4× under marisa-trie on single words, 4.9× on random pairs, 3.3× at 10 M — and exactly one byte per key above the bare ClosedHashIndex (1.26 against 0.26), which is the fingerprint that buys the membership check.
• Do the keys share a lot of structure (a path namespace, a versioned catalogue, a cross product)? Measure before choosing: that is where an FST can beat a keyless hash outright.
• A dict / HashMap is not in the table because it has no serialised form: 71–95 bytes per key above the key list across these corpora (58–60 at 10 M), rebuilt from the keys on every process start, where every structure here is mapped from a file.

Point-lookup latency vs the standard library

cargo run --release --example bench — 1 M real dictionary-word bigrams (word_i.word_j, mean key 10.9 bytes; never a synthetic entity-000…N sequence, which arrives pre-sorted and hash-degenerate). Measured 2026-09-12, the better of two runs back to back on a rested machine, each lookup cell the minimum of five passes after a warm-up (latency-rs-2026-09-12-arz-386b2e6.txt). Absolute numbers are one machine on one day — the std::HashMap control reads 295 ns here against 289 on the 2.0.0 table and 245 on 1.1.0, and StringIndex, unchanged since 0.5.1, is 1.32× of it against 1.47× and 1.30× there — so read the ratios within a column, and a shift under ~15 % between tables as the session.

Reading it: for a fixed / closed vocabulary, PerfectHashIndex::id_unchecked is the fastest structure in the table — 4.1× as quick as the SipHash HashMap and 2.4× an FxHash one — and compact and serialisable. CompactHashIndex::id keeps a probabilistic membership check and still beats the HashMap 2.2× on lookup, and builds in a fifth of its time. Verified id pays one extra cache line and a key compare; StringIndex trades latency for the queries a hash map cannot answer at all. The other Rust string indexes, the three-corpus table, the Python-level table against dict and marisa-trie, the 1 M / 10 M scale table and the protocol behind every number are in the benchmarks.

Security

Every loader is a safe fn on arbitrary bytes since 1.0: a crafted blob answers wrong ids, never out-of-range ones. The load_mmap family is what is unsafe, and its obligation is about the file, not the bytes. The checksums are integrity and not authentication, and the hashes are unseeded, so this is not a HashDoS defence — the threat model and the supported versions are in SECURITY.md.

Sponsoring

If lexindex saves memory or latency in a system you run, consider sponsoring its development. Using it in production? Corporate sponsorship funds what keeps a library like this dependable — compatibility across Rust and Python releases, the benchmark suite behind every number above, security hardening of the loaders, and performance work at hundreds of millions of keys — and tells the maintainer which workloads to measure next.

Prior art

The minimal perfect hash under the three hash indexes is in-crate and follows PHast's map-or-bump construction, the successor of PTHash: keys grouped into buckets by a first hash, a one-byte seed per bucket that slides the bucket's keys along a short slice of the table until every one lands on a free value, the buckets no seed places bumped to a smaller table under a fresh hash, and a remap that pulls every bumped key into a hole the first table left. Nothing is ever displaced, which is what makes the build one streaming pass over sorted hashes.

• Giulio Ermanno Pibiri and Roberto Trani, PTHash: Revisiting FCH Minimal Perfect Hashing, SIGIR 2021 — arXiv:2104.10402.
• Piotr Beling and Peter Sanders, PHast — Perfect Hashing with fast evaluation, 2025 — arXiv:2504.17918.
• Ragnar Groot Koerkamp, PtrHash: Minimal Perfect Hashing at RAM Throughput, 2025 — arXiv:2502.15539, ptr_hash.

Until 1.0 the perfect hash was ptr_hash. Its pilot table was serialised behind private fields, so a blob holding one could not be validated from outside the crate that owned it, and from_bytes and load_mmap had to be unsafe fn on both hash indexes; an MPH whose every array length is written and checked here makes those loaders safe, and that is the whole of the trade. 1.1's PHast-shaped table builds 10 M real word-bigram hashes in 49 ns/key on one thread (9 ns/key on eight) at 2.09 bits/key, against 280 ns/key and 2.39 bits for 1.0's, and its lookup costs 4.2 ns/key on in-order probes; the same-process comparison with ptr_hash and the PHast authors' ph crate is in the benchmarks.

License

MIT © Ilia Gradina