XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-4-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 22 12.48 13.00 112,276 MAX VALUE 22,519.60 2.51 0.20 2.34

Relational linkage 0.16 0.60 0.36 0.36 356.08 0.00 -1,049.20 0.06 0.18 1.88

Tightness 0.46 0.55 0.50 0.50 90.18 0.00 -124.55 0.02 0.04 3.71

Tuples 281 340 311.88 312.00 56,138 MAX VALUE 1,033.53 12.45 0.04 3.71

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 3 15 9.00 8.50 360 9.39e+36 85.13 3.15 0.35 2.38

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	22	12.48	13.00	112,276	MAX VALUE	22,519.60	2.51	0.20	2.34
Relational linkage	0.16	0.60	0.36	0.36	356.08	0.00	-1,049.20	0.06	0.18	1.88
Tightness	0.46	0.55	0.50	0.50	90.18	0.00	-124.55	0.02	0.04	3.71
Tuples	281	340	311.88	312.00	56,138	MAX VALUE	1,033.53	12.45	0.04	3.71
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	15	9.00	8.50	360	9.39e+36	85.13	3.15	0.35	2.38
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 21
Number of leaves: 12
Tree depth: 4
CIR: 0.12
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 3 60 21.81 15.00 458 2.20e+25 58.35 17.22 0.79 2.85

Variables per cluster 4 20 10.19 8.00 214 1.55e+20 46.49 4.80 0.47 2.15

Separator constraints 0 53 13.24 7.00 278 0 None 14.62 1.10 2.71

Separator variables 0 18 8.29 7.00 174 0 None 4.65 0.56 2.15

Clusters per var 1 12 5.35 5.50 214 4.15e+22 52.08 3.76 0.70 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	60	21.81	15.00	458	2.20e+25	58.35	17.22	0.79	2.85
Variables per cluster	4	20	10.19	8.00	214	1.55e+20	46.49	4.80	0.47	2.15
Separator constraints	0	53	13.24	7.00	278	0	None	14.62	1.10	2.71
Separator variables	0	18	8.29	7.00	174	0	None	4.65	0.56	2.15
Clusters per var	1	12	5.35	5.50	214	4.15e+22	52.08	3.76	0.70	2.14

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 149
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 31 361 125.84 109.00 4,782 MAX VALUE 174.80 86.10 0.68 3.46

Variables per cluster 10 84 28.21 21.50 1,072 MAX VALUE 120.29 18.26 0.65 3.14

Separator constraints 0 201 82.74 72.00 3,144 0 None 52.49 0.63 3.46

Separator variables 0 61 23.47 20.00 892 0 None 13.92 0.59 3.11

Clusters per variable 1 10 5.96 7.00 1,072 MAX VALUE 291.17 2.70 0.45 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	31	361	125.84	109.00	4,782	MAX VALUE	174.80	86.10	0.68	3.46
Variables per cluster	10	84	28.21	21.50	1,072	MAX VALUE	120.29	18.26	0.65	3.14
Separator constraints	0	201	82.74	72.00	3,144	0	None	52.49	0.63	3.46
Separator variables	0	61	23.47	20.00	892	0	None	13.92	0.59	3.11
Clusters per variable	1	10	5.96	7.00	1,072	MAX VALUE	291.17	2.70	0.45	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 147
Triangles: 143
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.50 0.27 0.27 10.79 0.00 None 0.10 0.38 3.32

Degree 3 15 9.00 8.50 360 9.39e+36 85.13 3.15 0.35 2.38

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.22 3.00 473 MAX VALUE 170.70 0.41 0.13 0.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.27	0.27	10.79	0.00	None	0.10	0.38	3.32
Degree	3	15	9.00	8.50	360	9.39e+36	85.13	3.15	0.35	2.38
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.22	3.00	473	MAX VALUE	170.70	0.41	0.13	0.52

Triangulated primal graph

Density: 46.67%
MCB compute time (ms): 9
MCB cycles: 331
Triangles: 2,001

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.62 1.00 0.84 0.80 33.42 0.00 -7.65 0.13 0.15 2.86

Degree 3 30 18.20 23.50 728 MAX VALUE 107.71 9.54 0.52 2.69

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 993 MAX VALUE 363.64 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.84	0.80	33.42	0.00	-7.65	0.13	0.15	2.86
Degree	3	30	18.20	23.50	728	MAX VALUE	107.71	9.54	0.52	2.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	993	MAX VALUE	363.64	0.00	0.00	0.00

Dual graph

Density: 10.17%
MCB compute time (ms): 390
MCB cycles: 1,706
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.45 0.74 0.52 0.50 93.90 0.00 -117.82 0.05 0.09 4.44

Degree 9 28 18.20 18.00 3,276 MAX VALUE 517.34 4.16 0.23 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.13 3.00 5,347 MAX VALUE 1,940.11 0.34 0.11 0.39

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.74	0.52	0.50	93.90	0.00	-117.82	0.05	0.09	4.44
Degree	9	28	18.20	18.00	3,276	MAX VALUE	517.34	4.16	0.23	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.13	3.00	5,347	MAX VALUE	1,940.11	0.34	0.11	0.39

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 72
MCB cycles: 141

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 6 3.56 3.00 640 MAX VALUE 224.00 0.78 0.22 1.15

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.66 7.00 939 MAX VALUE 265.67 1.00 0.15 1.40

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.00	0.00	0.00	0.00	0.00	None	0.00	None	0.00
Degree	2	6	3.56	3.00	640	MAX VALUE	224.00	0.78	0.22	1.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.66	7.00	939	MAX VALUE	265.67	1.00	0.15	1.40

Triangulated dual graph

Density: 44.79%
Triangles: 183,358

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.71 1.00 0.83 0.79 149.30 0.00 -34.68 0.09 0.11 4.71

Degree 9 124 80.18 93.00 14,432 MAX VALUE 751.88 40.24 0.50 3.78

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.83	0.79	149.30	0.00	-34.68	0.09	0.11	4.71
Degree	9	124	80.18	93.00	14,432	MAX VALUE	751.88	40.24	0.50	3.78
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.37%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.48 1.00 0.80 0.72 143.15 0.00 -44.89 0.16 0.20 3.29

Degree 2 65 20.36 7.00 3,664 MAX VALUE 417.51 22.20 1.09 3.16

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.80	0.72	143.15	0.00	-44.89	0.16	0.20	3.29
Degree	2	65	20.36	7.00	3,664	MAX VALUE	417.51	22.20	1.09	3.16
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-4-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 15 3.27 2.00 720 MAX VALUE 209.90 3.01 0.92 0.91

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.37 6.00 898 MAX VALUE 260.12 0.78 0.12 0.48

XCSP 2.1 Benchmarks