XCSP 2.1 Benchmark Database

Instance: normalized-ii-8d2-ext
Number of variables: 1860
Number of constraints: 7427
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 1860
Number of constraints: 7427

General features

Coarse blocks: 177,460
Value tables: 3,160

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

Arity 2 10 2.23 2.00 16,550 MAX VALUE 5,521.46 1.22 0.55 0.17

Coarse blocks size 1 512 11.15 4.00 1,978,170 MAX VALUE 242,983.00 49.51 4.44 1.64

Relational linkage 0.50 1.00 0.98 1.00 68,791.60 0.00 -2,236.14 0.10 0.10 0.35

Tightness 0.00 0.25 0.24 0.25 1,793.28 0.00 -11,471.60 0.05 0.19 0.17

Tuples 3 1,023 19.68 3.00 146,181 MAX VALUE 9,408.13 109.76 5.58 0.17

Values 2 2 2.00 2.00 3,720 MAX VALUE 1,289.25 0.00 0.00 0.00

Value table constraints 2 52 6.20 2.00 19,590 MAX VALUE 4,194.21 8.72 1.41 1.32

Value table partitions 2 128 22.29 2.00 70,440 MAX VALUE 6,127.42 32.99 1.48 1.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	10	2.23	2.00	16,550	MAX VALUE	5,521.46	1.22	0.55	0.17
Coarse blocks size	1	512	11.15	4.00	1,978,170	MAX VALUE	242,983.00	49.51	4.44	1.64
Relational linkage	0.50	1.00	0.98	1.00	68,791.60	0.00	-2,236.14	0.10	0.10	0.35
Tightness	0.00	0.25	0.24	0.25	1,793.28	0.00	-11,471.60	0.05	0.19	0.17
Tuples	3	1,023	19.68	3.00	146,181	MAX VALUE	9,408.13	109.76	5.58	0.17
Values	2	2	2.00	2.00	3,720	MAX VALUE	1,289.25	0.00	0.00	0.00
Value table constraints	2	52	6.20	2.00	19,590	MAX VALUE	4,194.21	8.72	1.41	1.32
Value table partitions	2	128	22.29	2.00	70,440	MAX VALUE	6,127.42	32.99	1.48	1.29

Tree decomposition

Number of clusters: 1,691
Number of leaves: 117
Tree depth: 28
CIR: 0.75
Independent Cluster Pairs: 1,073,790
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Tree1.json

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

Cluster constraints 1 203 5.79 5.00 9,794 MAX VALUE 1,909.39 14.03 2.42 1.28

Variables per cluster 2 157 28.97 15.00 48,993 MAX VALUE 5,134.13 25.34 0.87 2.11

Separator constraints 0 182 1.40 0.00 2,367 0 None 12.48 8.92 0.41

Separator variables 0 150 27.87 14.00 47,133 0 None 25.12 0.90 2.11

Clusters per var 1 505 26.34 11.00 48,993 MAX VALUE 4,090.17 68.39 2.60 2.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	203	5.79	5.00	9,794	MAX VALUE	1,909.39	14.03	2.42	1.28
Variables per cluster	2	157	28.97	15.00	48,993	MAX VALUE	5,134.13	25.34	0.87	2.11
Separator constraints	0	182	1.40	0.00	2,367	0	None	12.48	8.92	0.41
Separator variables	0	150	27.87	14.00	47,133	0	None	25.12	0.90	2.11
Clusters per var	1	505	26.34	11.00	48,993	MAX VALUE	4,090.17	68.39	2.60	2.61

Dual tree decomposition

Number of clusters: 1,790
Number of leaves: 800
Tree depth: 16
CIR: 0.88
Independent Cluster Pairs: 1,407,770
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/DualTree1.json

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

Cluster constraints 37 4,305 572.42 475.00 1,024,630 MAX VALUE 9,607.23 685.86 1.20 3.40

Variables per cluster 10 385 49.99 45.00 89,477 MAX VALUE 6,065.19 58.29 1.17 2.93

Separator constraints 0 2,421 481.90 431.00 862,610 0 None 505.24 1.05 3.38

Separator variables 0 292 45.84 44.00 82,050 0 None 48.02 1.05 2.94

Clusters per variable 1 111 12.05 13.00 89,477 MAX VALUE 16,334.30 8.90 0.74 2.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	4,305	572.42	475.00	1,024,630	MAX VALUE	9,607.23	685.86	1.20	3.40
Variables per cluster	10	385	49.99	45.00	89,477	MAX VALUE	6,065.19	58.29	1.17	2.93
Separator constraints	0	2,421	481.90	431.00	862,610	0	None	505.24	1.05	3.38
Separator variables	0	292	45.84	44.00	82,050	0	None	48.02	1.05	2.94
Clusters per variable	1	111	12.05	13.00	89,477	MAX VALUE	16,334.30	8.90	0.74	2.78

Primal graph

Density: 0.66%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Primal1.json

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

Clustering coefficient 0.00 0.80 None 0.38 None None None None None 1.11

Degree 1 52 12.34 10.00 22,950 MAX VALUE 4,414.42 8.91 0.72 1.47

Eccentricity 5 8 5.92 6.00 11,020 MAX VALUE 3,290.33 0.87 0.15 1.14

MCB cycle size 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	0.00	0.80	None	0.38	None	None	None	None	None	1.11
Degree	1	52	12.34	10.00	22,950	MAX VALUE	4,414.42	8.91	0.72	1.47
Eccentricity	5	8	5.92	6.00	11,020	MAX VALUE	3,290.33	0.87	0.15	1.14
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 3.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: None

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

Clustering coefficient 0.17 1.00 None 0.82 None None None None None 3.84

Degree 1 654 65.85 27.00 122,484 MAX VALUE 6,499.53 107.28 1.63 3.64

Eccentricity 3 5 3.65 4.00 6,786 MAX VALUE 2,381.13 0.62 0.17 0.91

MCB cycle size 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	0.17	1.00	None	0.82	None	None	None	None	None	3.84
Degree	1	654	65.85	27.00	122,484	MAX VALUE	6,499.53	107.28	1.63	3.64
Eccentricity	3	5	3.65	4.00	6,786	MAX VALUE	2,381.13	0.62	0.17	0.91
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.59%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,825,100
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.71 0.72 5,295.36 0.00 None 0.09 0.12 2.92

Degree 9 79 43.63 47.00 324,040 MAX VALUE 27,266.10 14.26 0.33 2.77

Eccentricity 5 8 6.05 6.00 44,930 MAX VALUE 13,342.60 0.52 0.09 0.69

MCB cycle size 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	0.00	1.00	0.71	0.72	5,295.36	0.00	None	0.09	0.12	2.92
Degree	9	79	43.63	47.00	324,040	MAX VALUE	27,266.10	14.26	0.33	2.77
Eccentricity	5	8	6.05	6.00	44,930	MAX VALUE	13,342.60	0.52	0.09	0.69
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.05%
MCB compute time (ms): None
MCB cycles: None

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

Clustering coefficient 0.00 0.30 0.00 0.00 25.71 0.00 None 0.03 8.31 0.10

Degree 2 10 3.72 4.00 27,600 MAX VALUE 9,601.65 0.86 0.23 0.87

Eccentricity 16 29 22.61 23.00 167,950 MAX VALUE 23,089.80 3.11 0.14 2.47

MCB cycle size 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	0.00	0.30	0.00	0.00	25.71	0.00	None	0.03	8.31	0.10
Degree	2	10	3.72	4.00	27,600	MAX VALUE	9,601.65	0.86	0.23	0.87
Eccentricity	16	29	22.61	23.00	167,950	MAX VALUE	23,089.80	3.11	0.14	2.47
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 0.69%

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

Clustering coefficient 0.12 1.00 0.80 0.75 5,936.33 0.00 -1,869.11 0.17 0.22 4.26

Degree 2 1,320 51.09 8.00 379,426 MAX VALUE 19,764.10 111.74 2.19 3.85

Eccentricity 4 7 5.31 5.00 39,411 MAX VALUE 12,343.20 0.62 0.12 0.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.12	1.00	0.80	0.75	5,936.33	0.00	-1,869.11	0.17	0.22	4.26
Degree	2	1,320	51.09	8.00	379,426	MAX VALUE	19,764.10	111.74	2.19	3.85
Eccentricity	4	7	5.31	5.00	39,411	MAX VALUE	12,343.20	0.62	0.12	0.94

Incidence graph

Density: 0.04%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8d2-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.25

Degree 1 52 3.56 2.00 33,100 MAX VALUE 8,666.67 5.52 1.55 0.67

Eccentricity 10 16 12.76 13.00 118,490 MAX VALUE 23,605.40 1.19 0.09 1.28

MCB cycle size None None None None None None None None None None

XCSP 2.1 Benchmarks