MyersBitParallel

A high-throughput C# implementation of the Myers bit-parallel Levenshtein distance algorithm, optimized for ASCII patterns up to 64 characters. Ships two engines:

• MyersBitParallel64 — full-string edit distance between two equal-ish length inputs.
• MyersSubstringBitParallel64 — best-match distance: the minimum edit distance between a short pattern and any contiguous substring of a longer haystack (a.k.a. semi-global / approximate substring search).

The single-word kernel evaluates one whole DP row per ulong operation, so distance computation is O(n) machine instructions instead of O(m·n) cell updates. For typical fuzzy-matching workloads (short query, many candidates, small allowed edit distance) it runs 5×–20× faster than a textbook Wagner-Fischer DP, and 20×–200× faster with the optional maxDist and requiredCharMask prefilters engaged.

Further reading: Optimizing Levenshtein for Fuzzy Name Matching — design notes, animations, and pruning layers.

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Features

• Single-word Myers bit-parallel kernel. Distance for ASCII patterns up to 64 characters in one ulong of state.
• Full-string and best-match substring modes. MyersBitParallel64 for end-to-end Levenshtein; MyersSubstringBitParallel64 for "find this fuzzy term inside this longer text" via a single-pass semi-global kernel.
• Pattern reuse as a first-class API. Prepare once, score many candidates without rebuilding the bit-mask table.
• Threshold-aware fuzzy search. Pass maxDist to short-circuit candidates that are guaranteed to be too far via length-difference, alphabet-overlap, and in-loop score cutoffs.
• Required-symbol filter. Pass requiredCharMask (built via BuildCharMask) to reject candidates that omit any pattern symbol before the kernel even runs.
• Configurable character mapping at construction time. Provide a Func<char, byte> that's invoked once per byte value to populate a 256-entry lookup table — the hot loop never invokes the delegate again.
• Built-in case-sensitive and case-insensitive engines as static readonly instances; no per-call allocation.
• Zero-allocation candidate paths via ArrayPool<T> for prepared pattern buffers.
• Multi-targets netstandard2.1 and net10.0.

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Installation

dotnet add package MyersBitParallel

Or in a .csproj:

<PackageReference Include="MyersBitParallel" Version="0.2.2" />

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Quick start

using MyersBitParallel;

// Use one of the built-in engines.
var engine = MyersBitParallel64.AsciiCaseInsensitive;

int distance = engine.Distance("kitten", "sitting"); // 3

SimilarityRatio sim = engine.SimilarityRatio("hello", "helo");
// sim.Distance == 1, sim.Ratio == 0.8

The two ready-made engines are:

Engine	Mapper	Behavior
MyersBitParallel64.AsciiCaseSensitive	AsciiMappers.CaseSensitive	Differences in case are significant
MyersBitParallel64.AsciiCaseInsensitive	AsciiMappers.CaseInsensitive	Folds A–Z to a–z

The engine itself is alphabet-agnostic — it operates on whatever byte bucket your Func<char, byte> mapper returns. The two statics above are convenience instances wired with the built-in AsciiMappers; build your own engine with new MyersBitParallel64(myMapper) for any other mapping you like.

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Reusing a pattern across many candidates

When you score one query against a large haystack, prepare the pattern once and pass it by in:

using MyersPattern64 pat = engine.Prepare("kitten");
foreach (string candidate in haystack)
{
    int d = engine.Distance(in pat, candidate);
    // ...
}
// `using` returns the rented bit-mask buffer to ArrayPool.Shared.

Per-candidate cost is just the bit-parallel kernel — no allocation, no mapper invocations, no rehashing.

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Threshold-aware fuzzy search

Pass maxDist to short-circuit any candidate whose distance is provably greater than the threshold. The engine uses the length-difference, the alphabet overlap, and an in-loop score - remaining cutoff to bail out as early as possible.

using MyersPattern64 pat = engine.Prepare("apple");

foreach (string candidate in haystack)
{
    int d = engine.Distance(in pat, candidate, maxDist: 2);
    if (d != int.MaxValue)
    {
        // candidate is within 2 edits of "apple"
    }
}

For an even stricter prefilter, supply a requiredCharMask listing the symbols every accepted candidate must contain. Build it from any reference string with BuildCharMask:

ulong required = engine.BuildCharMask("apple"); // pattern's char-mask

foreach (string candidate in haystack)
{
    int d = engine.Distance(in pat, candidate, maxDist: 2, requiredCharMask: required);
    if (d != int.MaxValue)
    {
        // candidate is within 2 edits AND contains every distinct symbol
        // that "apple" does (a, p, l, e).
    }
}

requiredCharMask is a 64-bit alphabet bitmap; mapped byte values are folded to the low 6 bits, so it's a conservative filter (it never wrongly rejects a valid match — at worst it lets a false positive through to the kernel, which then produces the correct answer). It becomes even more helpful if you generate your own engine with at most 64 distinct values.

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Best-match substring search

MyersSubstringBitParallel64 answers a different question than MyersBitParallel64: given a short pattern and a longer haystack, what's the minimum edit distance to any contiguous substring of the haystack? This is the "fuzzy find-in-string" operation — classically solved by semi-global DP filling an (m+1) × (n+1) matrix, here done in a single O(n) bit-parallel pass over the haystack.

using MyersBitParallel;

var engine = MyersSubstringBitParallel64.CaseInsensitive;

int d = engine.BestMatchDistance("BOAT", "THE LONG MOAT OF THE CASTLE");
// d == 1   (best window = "MOAT", one substitution)

int same = engine.BestMatchDistance("HELLO", "SAY HELLO WORLD");
// same == 0   (exact substring match)

int fuzzy = engine.BestMatchDistance("JSMITH", "USER_ID=JSMTH42");
// fuzzy == 1   (one deletion: "JSMTH")

Reuse a prepared pattern across many haystacks exactly like the full-string engine:

using MyersSubstringPattern64 pat = engine.Prepare("jsmith");
foreach (string row in logLines)
{
    if (engine.BestMatchDistance(in pat, row) <= 2)
    {
        // row contains something within 2 edits of "jsmith"
    }
}

Semantics in edge cases:

• BestMatchDistance("", text) is 0 — the empty substring always matches.
• BestMatchDistance(pattern, "") is pattern.Length.
• When pattern is longer than text, the result is the minimum Levenshtein distance between pattern and any substring of text (including the full text), bounded below by pattern.Length - text.Length. Useful for ranking short candidates against a longer query.

The engine exposes the same constructors, Prepare, CaseSensitive / CaseInsensitive statics, and 64-char pattern limit as MyersBitParallel64. Key methods:

int BestMatchDistance(string pattern, string text);
int BestMatchDistance(in MyersSubstringPattern64 pattern, string text);
MyersSubstringPattern64 Prepare(string query);

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Custom character mapper

Pass any Func<char, byte> to the engine's constructor. It's called once per byte value at construction time to build a 256-entry lookup table; the hot loop reads the table directly with no further delegate dispatch.

// Engine that treats every ASCII punctuation/whitespace character as
// equivalent (all collapsed to bucket 0). Letters are case-folded; digits
// are kept verbatim. Note: collapsing to a single bucket only erases the
// *identity* of those characters, not their position — both inputs still
// need to have the same length and the same shape.
var engine = new MyersBitParallel64(c =>
{
    if ((uint)(c - 'A') < 26u) return (byte)(c | 0x20); // fold A-Z to a-z
    if ((uint)(c - 'a') < 26u) return (byte)c;          // a-z verbatim
    if ((uint)(c - '0') < 10u) return (byte)c;          // 0-9 verbatim
    return 0;                                            // any non-alphanumeric
});

// Same length, same letter sequence; only the punctuation differs and
// every punctuation character maps to bucket 0, so distance is 0.
int same = engine.Distance("Hello, world!", "Hello& world?"); // 0

// Different lengths still cost edits — punctuation is collapsed, not deleted.
int diff = engine.Distance("Hello, world!", "hello world"); // 2

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API surface

Type	Description
MyersBitParallel64	Full-string engine: distance, similarity ratio, char-mask helper
MyersPattern64	Reusable prepared pattern for the full-string engine
MyersSubstringBitParallel64	Best-match substring engine
MyersSubstringPattern64	Reusable prepared pattern for the substring engine
SimilarityRatio	(int Distance, double Ratio) record struct
AsciiMappers.CaseSensitive / .CaseInsensitive	Built-in Func<char, byte> mappers

Key methods on MyersBitParallel64:

int Distance(string a, string b, int maxDist = int.MaxValue, ulong requiredCharMask = 0);
int Distance(in MyersPattern64 pattern, string candidate,
             int maxDist = int.MaxValue, ulong requiredCharMask = 0);

SimilarityRatio SimilarityRatio(string a, string b, int maxDist = int.MaxValue, ulong requiredCharMask = 0);
SimilarityRatio SimilarityRatio(in MyersPattern64 pattern, string candidate, int maxDist = int.MaxValue, ulong requiredCharMask = 0);

MyersPattern64 Prepare(string pattern);
ulong BuildCharMask(string s);

Distance returns int.MaxValue when the result is known to exceed maxDist; otherwise the true edit distance.

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Benchmarks

All benchmarks use BenchmarkDotNet with the ShortRun job; Ratio is each method's mean time divided by the fastest row (lower is better). Machine, runtime, and job settings affect absolute numbers; see the blog post for full tables and methodology.

Full-string distance (OneToManyMaxDist64Benchmark)

One prepared query, 1000 noisy ASCII candidates, case-insensitive distance, MyersBitParallel64.AsciiCaseInsensitive.

Method	MaxDist	CandidateCount	Mean	Ratio
Myers_PreparedOnce_WithMaxDist	3	1000	5.415 μs	1.00
Myers_PreparedOnce_NoMaxDist	3	1000	21.652 μs	4.00
NaiveLevenshteinReference_NoMaxDist	3	1000	202.914 μs	37.48
NaiveLevenshteinReference_WithMaxDist	3	1000	63.057 μs	11.65
WagnerFischerReference_WithMaxDist	3	1000	42.496 μs	7.85
UkkonenReference_WithMaxDist	3	1000	51.068 μs	9.43

Best-match substring search (OneToManyBestMatch64Benchmark)

Eight distinct ASCII queries each scored against HaystackCount haystacks (~10-word filler sentences with one noisy copy of the query embedded at a random offset). Case-insensitive; every reference is a fair apples-to-apples implementation of the same min-over-substrings quantity.

Method	HaystackCount	Mean	Ratio	Allocated
Myers_PreparedOnce	100	0.65 ms	1.00	0 B
Myers_PerCallPrepare	100	0.72 ms	1.10	0 B
SemiGlobal_TwoRow	100	5.16 ms	7.90	1,133 kB
SemiGlobal_FullMatrix	100	6.73 ms	10.29	5,091 kB
Myers_PreparedOnce	1000	6.91 ms	1.00	0 B
Myers_PerCallPrepare	1000	7.12 ms	1.03	0 B
SemiGlobal_TwoRow	1000	39.57 ms	5.73	11,315 kB
SemiGlobal_FullMatrix	1000	65.42 ms	9.47	50,834 kB

Measured on an Intel Core i5-12600K, .NET 10.0.5. The bit-parallel kernel is ~6–10× faster than an equivalent-semantics semi-global Wagner-Fischer and allocates zero bytes per call vs. tens of megabytes for the DP references.

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Limitations

• Single-byte alphabet. The engine maps each char to a single byte via your Func<char, byte> mapper. Anything that fits into 256 buckets works (ASCII, Latin-1, a custom Unicode-fold table, etc.); for full Unicode you'd have to pre-fold to a byte representation yourself, or wait for a future blocked-Myers Unicode kernel.
• Pattern length capped at 64 characters (the bit-vector is a single ulong). Both engines throw ArgumentException on longer patterns.
• Candidate / haystack length is unrestricted.

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Target frameworks

• netstandard2.1 — works on .NET Core 3.x, .NET 5+, Xamarin, Unity, Mono.
• net10.0 — uses in-box System.Numerics.BitOperations and other modern intrinsics for the popcount paths.

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License

GNU Affero General Public License v3.0