XCSP 2.1 Benchmark Database

Instance: normalized-ii-8a4-ext
Number of variables: 792
Number of constraints: 3134
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 792
Number of constraints: 3134

General features

Coarse blocks: 295,848
Value tables: 4,584

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

Arity 2 8 2.52 2.00 7,908 MAX VALUE 2,559.96 1.65 0.66 0.35

Coarse blocks size 1 128 9.68 4.00 2,863,400 MAX VALUE 517,510.00 16.12 1.67 1.77

Relational linkage 0.50 1.00 0.99 1.00 128,328.00 0.00 -1,414.52 0.06 0.06 0.25

Tightness 0.00 0.25 0.23 0.25 712.72 0.00 -5,481.41 0.07 0.31 0.35

Tuples 3 255 23.26 3.00 72,882 MAX VALUE 4,661.51 67.16 2.89 0.35

Values 2 2 2.00 2.00 1,584 MAX VALUE 548.97 0.00 0.00 0.00

Value table constraints 2 46 3.73 2.00 17,076 MAX VALUE 4,603.02 4.90 1.32 0.99

Value table partitions 2 128 28.24 16.00 129,432 MAX VALUE 12,493.30 30.41 1.08 1.81

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.52	2.00	7,908	MAX VALUE	2,559.96	1.65	0.66	0.35
Coarse blocks size	1	128	9.68	4.00	2,863,400	MAX VALUE	517,510.00	16.12	1.67	1.77
Relational linkage	0.50	1.00	0.99	1.00	128,328.00	0.00	-1,414.52	0.06	0.06	0.25
Tightness	0.00	0.25	0.23	0.25	712.72	0.00	-5,481.41	0.07	0.31	0.35
Tuples	3	255	23.26	3.00	72,882	MAX VALUE	4,661.51	67.16	2.89	0.35
Values	2	2	2.00	2.00	1,584	MAX VALUE	548.97	0.00	0.00	0.00
Value table constraints	2	46	3.73	2.00	17,076	MAX VALUE	4,603.02	4.90	1.32	0.99
Value table partitions	2	128	28.24	16.00	129,432	MAX VALUE	12,493.30	30.41	1.08	1.81

Tree decomposition

Number of clusters: 653
Number of leaves: 62
Tree depth: 30
CIR: 0.78
Independent Cluster Pairs: 166,184
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Tree1.json

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

Cluster constraints 0 281 10.62 5.00 6,932 0 None 30.39 2.86 1.84

Variables per cluster 7 103 18.60 14.00 12,143 MAX VALUE 1,715.49 17.00 0.91 2.01

Separator constraints 0 254 5.82 0.00 3,798 0 None 26.55 4.57 0.98

Separator variables 0 98 17.38 13.00 11,351 0 None 16.47 0.95 2.00

Clusters per var 1 242 15.33 7.00 12,143 MAX VALUE 1,547.12 28.95 1.89 2.99

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	281	10.62	5.00	6,932	0	None	30.39	2.86	1.84
Variables per cluster	7	103	18.60	14.00	12,143	MAX VALUE	1,715.49	17.00	0.91	2.01
Separator constraints	0	254	5.82	0.00	3,798	0	None	26.55	4.57	0.98
Separator variables	0	98	17.38	13.00	11,351	0	None	16.47	0.95	2.00
Clusters per var	1	242	15.33	7.00	12,143	MAX VALUE	1,547.12	28.95	1.89	2.99

Dual tree decomposition

Number of clusters: 750
Number of leaves: 306
Tree depth: 16
CIR: 0.83
Independent Cluster Pairs: 233,083
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/DualTree1.json

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

Cluster constraints 37 2,301 355.50 260.00 266,628 MAX VALUE 3,826.60 420.29 1.18 3.34

Variables per cluster 10 253 40.64 35.00 30,480 MAX VALUE 2,463.57 43.20 1.06 2.86

Separator constraints 0 1,494 282.81 201.00 212,106 0 None 308.08 1.09 3.32

Separator variables 0 182 36.46 33.00 27,346 0 None 34.97 0.96 2.87

Clusters per variable 1 56 9.73 10.00 30,480 MAX VALUE 6,345.88 6.16 0.63 2.75

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	2,301	355.50	260.00	266,628	MAX VALUE	3,826.60	420.29	1.18	3.34
Variables per cluster	10	253	40.64	35.00	30,480	MAX VALUE	2,463.57	43.20	1.06	2.86
Separator constraints	0	1,494	282.81	201.00	212,106	0	None	308.08	1.09	3.32
Separator variables	0	182	36.46	33.00	27,346	0	None	34.97	0.96	2.87
Clusters per variable	1	56	9.73	10.00	30,480	MAX VALUE	6,345.88	6.16	0.63	2.75

Primal graph

Density: 1.36%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Primal1.json

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

Clustering coefficient 0.00 0.80 0.35 0.33 275.33 0.00 None 0.35 1.01 1.11

Degree 6 46 10.74 9.00 8,508 MAX VALUE 1,765.88 7.18 0.67 1.60

Eccentricity 5 8 6.05 6.00 4,794 MAX VALUE 1,416.64 0.96 0.16 1.23

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	0.35	0.33	275.33	0.00	None	0.35	1.01	1.11
Degree	6	46	10.74	9.00	8,508	MAX VALUE	1,765.88	7.18	0.67	1.60
Eccentricity	5	8	6.05	6.00	4,794	MAX VALUE	1,416.64	0.96	0.16	1.23
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 6.27%
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 0.21 1.00 0.79 0.80 622.68 0.00 -206.88 0.14 0.18 3.84

Degree 6 363 49.57 23.00 39,256 MAX VALUE 2,555.27 66.09 1.33 3.77

Eccentricity 3 5 3.62 4.00 2,865 MAX VALUE 1,008.20 0.58 0.16 0.85

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	0.21	1.00	0.79	0.80	622.68	0.00	-206.88	0.14	0.18	3.84
Degree	6	363	49.57	23.00	39,256	MAX VALUE	2,555.27	66.09	1.33	3.77
Eccentricity	3	5	3.62	4.00	2,865	MAX VALUE	1,008.20	0.58	0.16	0.85
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 1.11%
MCB compute time (ms): None
MCB cycles: None
Triangles: 466,662
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Dual1.json

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

Clustering coefficient 0.00 0.86 0.66 0.64 2,054.93 0.00 None 0.12 0.18 2.87

Degree 6 57 34.79 35.00 109,044 MAX VALUE 10,816.50 12.04 0.35 2.60

Eccentricity 5 8 6.28 6.00 19,681 MAX VALUE 5,739.22 0.71 0.11 0.99

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	0.86	0.66	0.64	2,054.93	0.00	None	0.12	0.18	2.87
Degree	6	57	34.79	35.00	109,044	MAX VALUE	10,816.50	12.04	0.35	2.60
Eccentricity	5	8	6.28	6.00	19,681	MAX VALUE	5,739.22	0.71	0.11	0.99
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.12%
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 0.43 0.01 0.00 28.99 0.00 None 0.04 4.59 0.38

Degree 2 11 3.85 4.00 12,072 MAX VALUE 4,134.59 1.07 0.28 1.10

Eccentricity 12 18 15.74 16.00 49,324 MAX VALUE 8,627.89 1.23 0.08 1.61

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	0.43	0.01	0.00	28.99	0.00	None	0.04	4.59	0.38
Degree	2	11	3.85	4.00	12,072	MAX VALUE	4,134.59	1.07	0.28	1.10
Eccentricity	12	18	15.74	16.00	49,324	MAX VALUE	8,627.89	1.23	0.08	1.61
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: 1.29%

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

Clustering coefficient 0.20 1.00 0.79 0.74 2,476.87 0.00 -827.53 0.18 0.23 4.46

Degree 2 571 40.29 9.00 126,264 MAX VALUE 8,255.30 69.17 1.72 3.88

Eccentricity 4 7 5.25 5.00 16,458 MAX VALUE 5,173.83 0.64 0.12 0.98

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.20	1.00	0.79	0.74	2,476.87	0.00	-827.53	0.18	0.23	4.46
Degree	2	571	40.29	9.00	126,264	MAX VALUE	8,255.30	69.17	1.72	3.88
Eccentricity	4	7	5.25	5.00	16,458	MAX VALUE	5,173.83	0.64	0.12	0.98

Incidence graph

Density: 0.10%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a4-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 46 4.03 2.00 15,816 MAX VALUE 4,025.30 5.36 1.33 0.88

Eccentricity 10 16 13.06 13.00 51,272 MAX VALUE 10,065.70 1.38 0.11 1.52

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

XCSP 2.1 Benchmarks