XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-91-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 3 23 12.48 12.00 112,360 MAX VALUE 22,522.20 2.53 0.20 2.35

Relational linkage 0.12 0.52 0.35 0.36 352.52 0.00 -1,059.64 0.06 0.18 1.85

Tightness 0.45 0.55 0.50 0.50 90.11 0.00 -124.67 0.02 0.04 3.72

Tuples 284 342 312.11 312.00 56,180 MAX VALUE 1,033.67 11.87 0.04 3.72

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

Value table constraints 6 13 9.00 9.00 360 3.66e+37 86.49 2.35 0.26 2.00

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	3	23	12.48	12.00	112,360	MAX VALUE	22,522.20	2.53	0.20	2.35
Relational linkage	0.12	0.52	0.35	0.36	352.52	0.00	-1,059.64	0.06	0.18	1.85
Tightness	0.45	0.55	0.50	0.50	90.11	0.00	-124.67	0.02	0.04	3.72
Tuples	284	342	312.11	312.00	56,180	MAX VALUE	1,033.67	11.87	0.04	3.72
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	6	13	9.00	9.00	360	3.66e+37	86.49	2.35	0.26	2.00
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: 3
CIR: 0.05
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Tree1.json

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

Cluster constraints 8 45 20.05 16.00 421 6.01e+25 59.36 12.04 0.60 2.62

Variables per cluster 7 20 11.52 11.00 242 4.16e+21 49.78 4.52 0.39 2.18

Separator constraints 0 37 11.48 7.00 241 0 None 10.73 0.93 2.53

Separator variables 0 19 9.62 8.00 202 0 None 4.63 0.48 2.24

Clusters per var 1 14 6.05 5.50 242 7.49e+23 54.97 4.48 0.74 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	45	20.05	16.00	421	6.01e+25	59.36	12.04	0.60	2.62
Variables per cluster	7	20	11.52	11.00	242	4.16e+21	49.78	4.52	0.39	2.18
Separator constraints	0	37	11.48	7.00	241	0	None	10.73	0.93	2.53
Separator variables	0	19	9.62	8.00	202	0	None	4.63	0.48	2.24
Clusters per var	1	14	6.05	5.50	242	7.49e+23	54.97	4.48	0.74	2.16

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 146
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/DualTree1.json

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

Cluster constraints 30 304 118.26 102.50 4,494 MAX VALUE 173.91 72.97 0.62 3.49

Variables per cluster 11 78 28.50 22.50 1,083 MAX VALUE 121.27 17.58 0.62 3.21

Separator constraints 0 156 77.47 77.50 2,944 0 None 43.22 0.56 3.53

Separator variables 0 58 23.76 20.00 903 0 None 13.29 0.56 3.07

Clusters per variable 1 10 6.02 7.00 1,083 MAX VALUE 292.53 2.76 0.46 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	30	304	118.26	102.50	4,494	MAX VALUE	173.91	72.97	0.62	3.49
Variables per cluster	11	78	28.50	22.50	1,083	MAX VALUE	121.27	17.58	0.62	3.21
Separator constraints	0	156	77.47	77.50	2,944	0	None	43.22	0.56	3.53
Separator variables	0	58	23.76	20.00	903	0	None	13.29	0.56	3.07
Clusters per variable	1	10	6.02	7.00	1,083	MAX VALUE	292.53	2.76	0.46	2.23

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 168
Triangles: 115
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Primal1.json

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

Clustering coefficient 0.10 0.33 0.21 0.22 8.60 0.00 -63.25 0.06 0.28 3.07

Degree 6 13 9.00 9.00 360 3.66e+37 86.49 2.35 0.26 2.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.40 3.00 572 MAX VALUE 204.13 0.49 0.14 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.33	0.21	0.22	8.60	0.00	-63.25	0.06	0.28	3.07
Degree	6	13	9.00	9.00	360	3.66e+37	86.49	2.35	0.26	2.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.40	3.00	572	MAX VALUE	204.13	0.49	0.14	0.67

Triangulated primal graph

Density: 50.26%
MCB compute time (ms): 9
MCB cycles: 371
Triangles: 2,236

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

Clustering coefficient 0.63 1.00 0.83 0.81 33.26 0.00 -7.88 0.13 0.16 2.87

Degree 6 32 19.60 23.50 784 MAX VALUE 112.46 9.51 0.49 2.65

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,113 MAX VALUE 407.58 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.83	0.81	33.26	0.00	-7.88	0.13	0.16	2.87
Degree	6	32	19.60	23.50	784	MAX VALUE	112.46	9.51	0.49	2.65
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,113	MAX VALUE	407.58	0.00	0.00	0.00

Dual graph

Density: 9.62%
MCB compute time (ms): 182
MCB cycles: 2,307
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Dual1.json

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

Clustering coefficient 0.44 0.57 0.50 0.50 90.45 0.00 -124.09 0.03 0.05 4.08

Degree 10 23 17.22 17.00 3,100 MAX VALUE 508.99 3.18 0.18 2.50

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.49 3.00 8,041 MAX VALUE 2,843.34 0.66 0.19 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.57	0.50	0.50	90.45	0.00	-124.09	0.03	0.05	4.08
Degree	10	23	17.22	17.00	3,100	MAX VALUE	508.99	3.18	0.18	2.50
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.49	3.00	8,041	MAX VALUE	2,843.34	0.66	0.19	0.88

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 64
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.04 7.99 0.10

Degree 2 6 3.56 3.00 640 MAX VALUE 224.13 0.76 0.21 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.71 7.00 946 MAX VALUE 266.22 1.11 0.17 1.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.04	7.99	0.10
Degree	2	6	3.56	3.00	640	MAX VALUE	224.13	0.76	0.21	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.71	7.00	946	MAX VALUE	266.22	1.11	0.17	1.49

Triangulated dual graph

Density: 44.25%
Triangles: 175,850

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

Clustering coefficient 0.67 1.00 0.83 0.80 148.72 0.00 -35.58 0.10 0.12 4.66

Degree 10 130 79.21 97.50 14,258 MAX VALUE 751.44 39.29 0.50 4.05

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	0.67	1.00	0.83	0.80	148.72	0.00	-35.58	0.10	0.12	4.66
Degree	10	130	79.21	97.50	14,258	MAX VALUE	751.44	39.29	0.50	4.05
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.53%

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

Clustering coefficient 0.51 1.00 0.79 0.73 142.73 0.00 -45.15 0.15 0.20 3.32

Degree 2 64 20.63 7.00 3,714 MAX VALUE 418.03 22.73 1.10 3.13

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	0.51	1.00	0.79	0.73	142.73	0.00	-45.15	0.15	0.20	3.32
Degree	2	64	20.63	7.00	3,714	MAX VALUE	418.03	22.73	1.10	3.13
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-2-40-25-180-500-91-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-91-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 13 3.27 2.00 720 MAX VALUE 211.26 2.88 0.88 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.58 6.00 928 MAX VALUE 264.43 0.91 0.14 0.60

XCSP 2.1 Benchmarks