Performance Benchmark Report

Statistical Metric: Median

Summary Table

Algorithm	Distance Type	Hyperparameters	Rust	Cython	Python	Rust/Cython	Rust/Python
discret_frechet	euclidean	eps=None; g=None	0.0008ms	0.0086ms	0.4842ms	10.75x	605.25x
dtw	euclidean	eps=None; g=None	0.0008ms	0.0082ms	0.4890ms	10.25x	611.19x
dtw	spherical	eps=None; g=None	0.0038ms	0.0109ms	0.3908ms	2.87x	102.86x
edr	euclidean	eps=0.01; g=None	0.0011ms	0.0074ms	0.3277ms	6.73x	297.96x
edr	spherical	eps=0.01; g=None	0.0038ms	0.0103ms	0.2216ms	2.71x	58.32x
erp	euclidean	eps=None; g=[-122.41443, 37.77646]	0.0017ms	0.0224ms	0.2953ms	13.21x	173.71x
erp	spherical	eps=None; g=[-122.41443, 37.77646]	0.0050ms	0.0297ms	0.8735ms	5.93x	174.71x
hausdorff	euclidean	eps=None; g=None	0.0013ms	0.0284ms	0.4785ms	21.85x	368.12x
hausdorff	spherical	eps=None; g=None	0.0316ms	0.0929ms	1.4050ms	2.94x	44.53x
lcss	euclidean	eps=0.01; g=None	0.0006ms	0.0072ms	0.3646ms	12.00x	607.58x
lcss	spherical	eps=0.01; g=None	0.0030ms	0.0102ms	0.1888ms	3.34x	61.90x
sspd	euclidean	eps=None; g=None	0.0023ms	0.0199ms	0.4758ms	8.65x	206.87x
sspd	spherical	eps=None; g=None	0.0451ms	0.1005ms	1.9232ms	2.23x	42.64x

Detailed Statistics

DISCRET_FRECHET (euclidean)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0008	0.0009	0.0004	0.0005	0.0081	46.89
CYTHON	0.0086	0.0095	0.0037	0.0039	0.0401	38.85
PYTHON	0.4842	0.5182	0.2172	0.1910	1.3931	41.90

Performance Improvement

Rust vs Cython: 10.75x
Rust vs Python: 605.25x

DTW (euclidean)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0008	0.0008	0.0003	0.0005	0.0046	32.95
CYTHON	0.0082	0.0093	0.0053	0.0043	0.0888	57.23
PYTHON	0.4890	0.5229	0.2236	0.1874	1.3917	42.75

Performance Improvement

Rust vs Cython: 10.25x
Rust vs Python: 611.19x

DTW (spherical)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0038	0.0039	0.0014	0.0017	0.0122	36.69
CYTHON	0.0109	0.0124	0.0058	0.0054	0.0684	46.80
PYTHON	0.3908	0.4301	0.1957	0.1475	1.4195	45.51

Performance Improvement

Rust vs Cython: 2.87x
Rust vs Python: 102.86x

EDR (euclidean)

Hyperparameters: eps=0.01; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0011	0.0012	0.0011	0.0006	0.0208	89.89
CYTHON	0.0074	0.0082	0.0033	0.0036	0.0289	40.67
PYTHON	0.3277	0.3677	0.1702	0.1394	0.9708	46.29

Performance Improvement

Rust vs Cython: 6.73x
Rust vs Python: 297.96x

EDR (spherical)

Hyperparameters: eps=0.01; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0038	0.0042	0.0017	0.0018	0.0139	40.37
CYTHON	0.0103	0.0118	0.0075	0.0048	0.1410	64.00
PYTHON	0.2216	0.2452	0.1143	0.0852	0.7367	46.60

Performance Improvement

Rust vs Cython: 2.71x
Rust vs Python: 58.32x

ERP (euclidean)

Hyperparameters: eps=None; g=[-122.41443, 37.77646]

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0017	0.0019	0.0013	0.0013	0.0234	65.97
CYTHON	0.0224	0.0249	0.0132	0.0107	0.1869	52.80
PYTHON	0.2953	0.3671	0.4784	0.1266	6.5803	130.30

Performance Improvement

Rust vs Cython: 13.21x
Rust vs Python: 173.71x

ERP (spherical)

Hyperparameters: eps=None; g=[-122.41443, 37.77646]

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0050	0.0055	0.0020	0.0028	0.0172	35.80
CYTHON	0.0297	0.0328	0.0147	0.0131	0.1469	44.86
PYTHON	0.8735	1.0177	0.5379	0.3410	4.6360	52.86

Performance Improvement

Rust vs Cython: 5.93x
Rust vs Python: 174.71x

HAUSDORFF (euclidean)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0013	0.0015	0.0012	0.0008	0.0241	81.42
CYTHON	0.0284	0.0286	0.0092	0.0121	0.0703	32.28
PYTHON	0.4785	0.5642	0.3286	0.1530	3.9326	58.25

Performance Improvement

Rust vs Cython: 21.85x
Rust vs Python: 368.12x

HAUSDORFF (spherical)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0316	0.0359	0.0173	0.0119	0.0940	48.27
CYTHON	0.0929	0.1066	0.0588	0.0355	0.3418	55.15
PYTHON	1.4050	1.5799	0.7753	0.4739	5.8188	49.07

Performance Improvement

Rust vs Cython: 2.94x
Rust vs Python: 44.53x

LCSS (euclidean)

Hyperparameters: eps=0.01; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0006	0.0007	0.0011	0.0005	0.0250	149.19
CYTHON	0.0072	0.0084	0.0042	0.0036	0.0370	50.36
PYTHON	0.3646	0.4130	0.2455	0.1461	3.1617	59.45

Performance Improvement

Rust vs Cython: 12.00x
Rust vs Python: 607.58x

LCSS (spherical)

Hyperparameters: eps=0.01; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0030	0.0034	0.0013	0.0015	0.0081	39.18
CYTHON	0.0102	0.0127	0.0345	0.0047	0.7768	271.50
PYTHON	0.1888	0.2150	0.1201	0.0665	0.9492	55.84

Performance Improvement

Rust vs Cython: 3.34x
Rust vs Python: 61.90x

SSPD (euclidean)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0023	0.0026	0.0013	0.0011	0.0179	50.55
CYTHON	0.0199	0.0215	0.0076	0.0123	0.1061	35.40
PYTHON	0.4758	0.5536	0.3039	0.1809	2.2450	54.89

Performance Improvement

Rust vs Cython: 8.65x
Rust vs Python: 206.87x

SSPD (spherical)

Hyperparameters: eps=None; g=None

Time Statistics

Implementation	Median (ms)	Mean (ms)	Std Dev (ms)	Min (ms)	Max (ms)	CV (%)
RUST	0.0451	0.0502	0.0259	0.0190	0.2020	51.47
CYTHON	0.1005	0.1133	0.0502	0.0474	0.3043	44.28
PYTHON	1.9232	2.1274	0.9684	0.6251	5.6920	45.52

Performance Improvement

Rust vs Cython: 2.23x
Rust vs Python: 42.64x

Analysis by Algorithm

Performance comparison across different implementations for each algorithm:

DISCRET_FRECHET

Rust vs Cython: Average improvement 10.75x (range: 10.75x - 10.75x)
Rust vs Python: Average improvement 605.25x (range: 605.25x - 605.25x)

DTW

Rust vs Cython: Average improvement 6.56x (range: 2.87x - 10.25x)
Rust vs Python: Average improvement 357.02x (range: 102.86x - 611.19x)

EDR

Rust vs Cython: Average improvement 4.72x (range: 2.71x - 6.73x)
Rust vs Python: Average improvement 178.14x (range: 58.32x - 297.96x)

ERP

Rust vs Cython: Average improvement 9.57x (range: 5.93x - 13.21x)
Rust vs Python: Average improvement 174.21x (range: 173.71x - 174.71x)

HAUSDORFF

Rust vs Cython: Average improvement 12.40x (range: 2.94x - 21.85x)
Rust vs Python: Average improvement 206.32x (range: 44.53x - 368.12x)

LCSS

Rust vs Cython: Average improvement 7.67x (range: 3.34x - 12.00x)
Rust vs Python: Average improvement 334.74x (range: 61.90x - 607.58x)

SSPD

Rust vs Cython: Average improvement 5.44x (range: 2.23x - 8.65x)
Rust vs Python: Average improvement 124.76x (range: 42.64x - 206.87x)

Analysis by Distance Type

Performance comparison across different distance types:

EUCLIDEAN Distance

Rust vs Cython: Average improvement 11.92x (range: 6.73x - 21.85x)
Rust vs Python: Average improvement 410.09x (range: 173.71x - 611.19x)
Best Performance Improvement Algorithm: hausdorff (21.85x)

SPHERICAL Distance

Rust vs Cython: Average improvement 3.34x (range: 2.23x - 5.93x)
Rust vs Python: Average improvement 80.83x (range: 42.64x - 174.71x)
Best Performance Improvement Algorithm: erp (5.93x)

Overall Statistics

RUST overall average time: 0.0078 ms
CYTHON overall average time: 0.0274 ms
PYTHON overall average time: 0.6091 ms
Rust vs Cython overall average improvement: 3.53x
Rust vs Python overall average improvement: 78.47x

Batch Computation Performance

Performance comparison for batch distance computation (pdist and cdist):

Test Configuration

Algorithm: dtw
Number of trajectories: 5 (fixed)
pdist computation: 10 distances (5×4/2)
Trajectory lengths tested: 10, 100, 1000 points
Distance types: euclidean, spherical

pdist Performance

Performance for pairwise distance computation (compressed distance matrix) with varying trajectory lengths:

Distance Type	Traj Length	Distances	Cython (ms)	Rust Seq (ms)	Rust Par (ms)	Speedup (Seq)	Speedup (Par)	Parallel Efficiency
euclidean	10	10	0.0902	0.0054	0.6141	16.70x	0.15x	0.009x
euclidean	100	10	6.3308	0.4340	0.8140	14.59x	7.78x	0.533x
euclidean	1000	10	626.1093	42.7020	7.4122	14.66x	84.47x	5.761x
spherical	10	10	0.1348	0.0649	0.6308	2.08x	0.21x	0.103x
spherical	100	10	13.2197	5.4938	1.7841	2.41x	7.41x	3.079x
spherical	1000	10	1029.9823	471.6477	85.0858	2.18x	12.11x	5.543x

cdist Performance

Performance for distance computation between two trajectory collections with varying trajectory lengths:

Distance Type	Traj Length	Distances	Cython (ms)	Rust Seq (ms)	Rust Par (ms)	Speedup (Seq)	Speedup (Par)	Parallel Efficiency
euclidean	10	25	0.1924	0.0120	0.1381	16.03x	1.39x	0.087x
euclidean	100	25	15.3446	1.0641	0.6353	14.42x	24.15x	1.675x
euclidean	1000	25	1521.2707	92.2849	26.5950	16.48x	57.20x	3.470x
spherical	10	25	0.8238	0.1291	0.4425	6.38x	1.86x	0.292x
spherical	100	25	25.5498	13.2348	4.2448	1.93x	6.02x	3.118x
spherical	1000	25	2553.6417	1186.0862	316.9027	2.15x	8.06x	3.743x

Batch Computation Summary

Euclidean Distance:

pdist - Rust (sequential) vs Cython: Average 15.32x speedup (range: 14.59x - 16.70x)
pdist - Rust (parallel) vs Cython: Average 30.80x speedup (range: 0.15x - 84.47x)
cdist - Rust (sequential) vs Cython: Average 15.65x speedup (range: 14.42x - 16.48x)
cdist - Rust (parallel) vs Cython: Average 27.58x speedup (range: 1.39x - 57.20x)

Spherical Distance:

pdist - Rust (sequential) vs Cython: Average 2.22x speedup (range: 2.08x - 2.41x)
pdist - Rust (parallel) vs Cython: Average 6.58x speedup (range: 0.21x - 12.11x)
cdist - Rust (sequential) vs Cython: Average 3.49x speedup (range: 1.93x - 6.38x)
cdist - Rust (parallel) vs Cython: Average 5.31x speedup (range: 1.86x - 8.06x)

Note: Parallel efficiency measures how much faster the parallel implementation is compared to the sequential implementation. For small datasets, parallel overhead may outweigh benefits.