[Run] Replace WindowWalker's brute-force fuzzy matching algorithm with optimal DP solution

[daverayment]

Summary of the Pull Request

Window Walker's fuzzy string matching algorithm exhibits exponential memory usage and execution time when given inputs containing repeated characters or phrases. When a user has several windows open with long titles (such as browser windows), it is straightforward to trigger a pathological case which uses up gigabytes of memory and freezes the UI. This is exacerbated by Run's lack of thread pruning, meaning work triggered by older keystrokes consumes CPU and memory until completion.

PR Checklist

• Closes: [Run] Exponential memory usage in Window Walker fuzzy matching with repeated characters/words #44546
• Closes: Power Toys.RUN is Consuming 17GB RAM #44184
• Communication: I've discussed this with core contributors already. If the work hasn't been agreed, this work might be rejected
• Tests: Added/updated and all pass
• Localization: All end-user-facing strings can be localized
• Dev docs: Added/updated
• New binaries: Added on the required places
  • JSON for signing for new binaries
  • WXS for installer for new binaries and localization folder
  • YML for CI pipeline for new test projects
  • YML for signed pipeline
• Documentation updated: If checked, please file a pull request on our docs repo and link it here: #xxx

Detailed Description of the Pull Request / Additional comments

The existing algorithm in FuzzyMatching.cs is greedy, creating all possible matching combinations of the search string within the candidate via its GetAllMatchIndexes() method. After this, it selects the best match and discards the others. This may be considered reasonable for small search strings, but it causes a combinatorial explosion when there are multiple possible matches where characters or substrings repeat, even when the search string is small.

The current brute-force algorithm has time complexity of O(n * m * C(n,m)) where C(n,m) = n!/(m!(n-m)!) and space complexity of O(C(n,m) * m) because it stores all possible match combinations before choosing the best.

For example, matching "eeee" in "eeeeeeee" creates C(8,4) = 70 match combinations, which stores 70 lists with 4 integers each, plus overhead from the LINQ-based list copying and appending:

var tempList = results
    .Where(x => x.Count == secondIndex && x[x.Count - 1] < firstIndex)
    .Select(x => x.ToList())   // Creates a full copy of each matching path
    .ToList();                 // Materializes all copies

results.AddRange(tempList);    // Adds lists to results

Each potential sub-match may be recalculated many times.

Window Walker queries across all window titles, so this problem will be magnified if the search text happens to match multiple titles and/or if a search string containing a single repeated character is used. For browser windows, where titles may be long, this is especially problematic, and similarly for Explorer windows with longer paths.

Proposed solution

The solution presented here is to use a dynamic programming algorithm which finds the optimal match directly without generating all possibilities.

In terms of complexity, the new algorithm benefits from a single pass through its DP table and only has to store two integer arrays which are sized proportionally to the search and candidate text string lengths; so O(n * m) for both time and space, i.e. polynomial instead of exponential.

Scoring is equivalent between the old and new algorithms, based strictly on the minimum match span within the candidate string.

Implementation notes

The new algorithm tracks the best start index for matches ending at each position, eliminating the need to store all possible paths. By storing the "latest best match so far" as you scan through the search text, you are guaranteed to minimise the span length. To recreate the best match, a separate table of parent indexes is kept and iterated backwards once the DP step is complete. Reversing this provides you with the same result (or equivalent if there are multiple best matches) as the original algorithm.

For this "minimum-span" fuzzy matching method, this should be optimal as it only scans once and storage is proportional to the search and candidate strings only.

Benchmarks

A verification and benchmarking suite is here: https://github.com/daverayment/WindowWalkerBench

Results from comparing the old and new algorithms are here: https://docs.google.com/spreadsheets/d/1eXmmnN2eI3774QxXXyx1Dv4SKu78U96q28GYnpHT0_8/edit?usp=sharing

Method	Mean	Error	StdDev	Ratio	RatioSD	Gen0	Gen1	Gen2	Allocated	Alloc Ratio
Old_Normal	4,034.4 ns	220.94 ns	647.98 ns	1.02	0.23	1.9760	-	-	8.09 KB	1.00
New_Normal	804.5 ns	24.29 ns	70.47 ns	0.20	0.04	0.4339	-	-	1.77 KB	0.22
Old_Repetitive	7,624.7 ns	318.06 ns	912.57 ns	1.94	0.38	3.7079	-	-	15.16 KB	1.87
New_Repetitive	2,714.6 ns	109.03 ns	318.03 ns	0.69	0.13	1.6403	-	-	6.72 KB	0.83
Old_Explosion	881,443,209.3 ns	26,273,980.96 ns	76,225,588.43 ns	223,872.87	39,357.31	50000.0000	27000.0000	5000.0000	351885.11 KB	43,518.16
New_Explosion	3,225.4 ns	111.98 ns	315.84 ns	0.82	0.15	1.7738	-	-	7.26 KB	0.90
Old_Explosion_8	460,153,862.6 ns	18,744,417.95 ns	54,974,137.06 ns	116,871.93	22,719.87	25000.0000	14000.0000	3000.0000	173117.13 KB	21,409.65
New_Explosion_8	2,958.3 ns	78.16 ns	230.45 ns	0.75	0.13	1.5793	-	-	6.46 KB	0.80
Old_Explosion_7	189,069,384.8 ns	3,774,916.46 ns	6,202,296.49 ns	48,020.68	7,501.98	11000.0000	6333.3333	2000.0000	71603.96 KB	8,855.37
New_Explosion_7	2,667.5 ns	117.69 ns	337.68 ns	0.68	0.13	1.3924	-	-	5.7 KB	0.70
Old_Explosion_6	71,960,114.8 ns	1,757,017.15 ns	5,125,301.87 ns	18,276.75	3,083.86	4500.0000	2666.6667	1333.3333	25515.96 KB	3,155.60
New_Explosion_6	2,232.5 ns	72.65 ns	202.52 ns	0.57	0.10	1.1978	-	-	4.91 KB	0.61
Old_Explosion_5	9,121,126.4 ns	180,744.42 ns	228,583.84 ns	2,316.62	358.55	1000.0000	968.7500	484.3750	7630.49 KB	943.67
New_Explosion_5	1,917.3 ns	48.63 ns	133.95 ns	0.49	0.08	1.0109	-	-	4.13 KB	0.51
Old_Explosion_4	2,489,593.2 ns	82,937.33 ns	236,624.90 ns	632.32	113.96	281.2500	148.4375	74.2188	1729.71 KB	213.92
New_Explosion_4	1,598.3 ns	51.92 ns	152.28 ns	0.41	0.07	0.8163	-	-	3.34 KB	0.41
Old_Explosion_3	202,814.0 ns	7,684.44 ns	22,293.96 ns	51.51	9.72	72.7539	0.2441	-	298.13 KB	36.87
New_Explosion_3	1,222.5 ns	26.07 ns	76.45 ns	0.31	0.05	0.6275	-	-	2.57 KB	0.32
Old_Subsequence	419,417.7 ns	8,308.97 ns	22,178.33 ns	106.53	17.23	266.6016	0.9766	-	1090.05 KB	134.81
New_Subsequence	2,501.9 ns	80.91 ns	233.43 ns	0.64	0.11	1.3542	-	-	5.55 KB	0.69

(Where "Old_Explosion" is "e" repeated 9 times. Times in nanoseconds or one millionth of a millisecond.)

It is worth noting that the results show a single string match. So matching "eeeeee" against a 99-character string took 25 MB of memory and 71 milliseconds to compute. For the new algorithm, this is reduced down to <5KB and 0.002 milliseconds. Even for a three-character repetition, the new algorithm is >150x faster with <1% of the allocations.

Real world example

Before (results still pending after more than a minute):

After (instantaneous results):

Validation Steps Performed

The verification tests in the benchmark project pass, with results identical to the original across a number of test cases, including the pathological cases identified earlier and edge cases such as single-character searches.

All unit tests under Wox.Test, including all 38 FuzzyMatcherTest entries still pass.

[crutkas]

This is 🔥🔥🔥🔥🔥🔥