XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-95-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 21 12.47 12.00 112,202 MAX VALUE 22,515.40 2.50 0.20 2.33

Relational linkage 0.12 0.56 0.35 0.36 354.56 0.00 -1,052.55 0.06 0.17 1.84

Tightness 0.44 0.56 0.50 0.50 90.24 0.00 -124.43 0.02 0.04 3.70

Tuples 276 353 311.67 312.00 56,101 MAX VALUE 1,033.41 12.37 0.04 3.70

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

Value table constraints 5 14 9.00 9.50 360 3.22e+37 86.37 2.38 0.26 2.14

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	21	12.47	12.00	112,202	MAX VALUE	22,515.40	2.50	0.20	2.33
Relational linkage	0.12	0.56	0.35	0.36	354.56	0.00	-1,052.55	0.06	0.17	1.84
Tightness	0.44	0.56	0.50	0.50	90.24	0.00	-124.43	0.02	0.04	3.70
Tuples	276	353	311.67	312.00	56,101	MAX VALUE	1,033.41	12.37	0.04	3.70
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	14	9.00	9.50	360	3.22e+37	86.37	2.38	0.26	2.14
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: 20
Number of leaves: 11
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Tree1.json

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

Cluster constraints 7 60 20.65 15.50 413 4.69e+24 56.81 14.20 0.69 2.76

Variables per cluster 6 21 10.95 10.00 219 1.29e+20 46.30 4.50 0.41 2.25

Separator constraints 0 42 11.65 8.00 233 0 None 11.10 0.95 2.62

Separator variables 0 18 8.95 7.50 179 0 None 4.38 0.49 2.25

Clusters per var 1 12 5.47 5.00 219 2.80e+23 53.99 3.76 0.69 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	60	20.65	15.50	413	4.69e+24	56.81	14.20	0.69	2.76
Variables per cluster	6	21	10.95	10.00	219	1.29e+20	46.30	4.50	0.41	2.25
Separator constraints	0	42	11.65	8.00	233	0	None	11.10	0.95	2.62
Separator variables	0	18	8.95	7.50	179	0	None	4.38	0.49	2.25
Clusters per var	1	12	5.47	5.00	219	2.80e+23	53.99	3.76	0.69	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 128
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/DualTree1.json

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

Cluster constraints 20 377 120.89 103.50 4,594 MAX VALUE 174.45 79.54 0.66 3.42

Variables per cluster 9 86 28.58 21.50 1,086 MAX VALUE 121.15 18.25 0.64 3.09

Separator constraints 0 193 80.03 75.00 3,041 0 None 47.50 0.59 3.43

Separator variables 0 63 23.84 20.00 906 0 None 13.89 0.58 3.00

Clusters per variable 1 10 6.03 7.00 1,086 MAX VALUE 293.11 2.72 0.45 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	20	377	120.89	103.50	4,594	MAX VALUE	174.45	79.54	0.66	3.42
Variables per cluster	9	86	28.58	21.50	1,086	MAX VALUE	121.15	18.25	0.64	3.09
Separator constraints	0	193	80.03	75.00	3,041	0	None	47.50	0.59	3.43
Separator variables	0	63	23.84	20.00	906	0	None	13.89	0.58	3.00
Clusters per variable	1	10	6.03	7.00	1,086	MAX VALUE	293.11	2.72	0.45	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 158
Triangles: 120
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Primal1.json

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

Clustering coefficient 0.07 0.40 0.24 0.23 9.62 0.00 -59.57 0.08 0.34 3.33

Degree 5 14 9.00 9.50 360 3.22e+37 86.37 2.38 0.26 2.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.32 3.00 524 MAX VALUE 187.97 0.47 0.14 0.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.40	0.24	0.23	9.62	0.00	-59.57	0.08	0.34	3.33
Degree	5	14	9.00	9.50	360	3.22e+37	86.37	2.38	0.26	2.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.32	3.00	524	MAX VALUE	187.97	0.47	0.14	0.62

Triangulated primal graph

Density: 49.87%
MCB compute time (ms): 6
MCB cycles: 400
Triangles: 2,233

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

Clustering coefficient 0.64 1.00 0.83 0.82 33.32 0.00 -7.74 0.12 0.15 2.96

Degree 5 31 19.45 24.00 778 MAX VALUE 111.97 9.42 0.48 2.80

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,200 MAX VALUE 439.44 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.83	0.82	33.32	0.00	-7.74	0.12	0.15	2.96
Degree	5	31	19.45	24.00	778	MAX VALUE	111.97	9.42	0.48	2.80
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,200	MAX VALUE	439.44	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 395
MCB cycles: 1,497
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Dual1.json

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

Clustering coefficient 0.43 0.64 0.51 0.50 90.90 0.00 -123.28 0.03 0.06 4.14

Degree 8 25 17.26 17.50 3,106 MAX VALUE 509.54 3.09 0.18 2.48

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.10 3.00 4,645 MAX VALUE 1,688.73 0.31 0.10 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.64	0.51	0.50	90.90	0.00	-123.28	0.03	0.06	4.14
Degree	8	25	17.26	17.50	3,106	MAX VALUE	509.54	3.09	0.18	2.48
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.10	3.00	4,645	MAX VALUE	1,688.73	0.31	0.10	0.34

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 68
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.37 0.00 None 0.02 7.94 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 223.92 0.78 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.72 7.00 948 MAX VALUE 266.69 1.06 0.16 1.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.37	0.00	None	0.02	7.94	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	223.92	0.78	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.72	7.00	948	MAX VALUE	266.69	1.06	0.16	1.42

Triangulated dual graph

Density: 45.27%
Triangles: 188,724

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

Clustering coefficient 0.71 1.00 0.83 0.80 149.72 0.00 -34.11 0.09 0.10 4.68

Degree 8 125 81.03 95.00 14,586 MAX VALUE 753.86 40.72 0.50 3.87

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	0.80	149.72	0.00	-34.11	0.09	0.10	4.68
Degree	8	125	81.03	95.00	14,586	MAX VALUE	753.86	40.72	0.50	3.87
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.24%

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

Clustering coefficient 0.54 1.00 0.80 0.72 143.42 0.00 -44.34 0.16 0.20 3.23

Degree 2 65 20.11 7.00 3,620 MAX VALUE 413.70 22.31 1.11 3.10

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	0.54	1.00	0.80	0.72	143.42	0.00	-44.34	0.16	0.20	3.23
Degree	2	65	20.11	7.00	3,620	MAX VALUE	413.70	22.31	1.11	3.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-95-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 14 3.27 2.00 720 MAX VALUE 211.13 2.88 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.47 6.00 912 MAX VALUE 262.13 0.85 0.13 0.54

XCSP 2.1 Benchmarks