XCSP 2.1 Benchmark Database

Instance: normalized-ii-8e2-ext
Number of variables: 1740
Number of constraints: 6971
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 1740
Number of constraints: 6971

General features

Coarse blocks: 277,920
Value tables: 4,720

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

Arity 2 10 2.31 2.00 16,130 MAX VALUE 5,320.50 1.40 0.60 0.22

Coarse blocks size 1 512 11.14 4.00 3,096,780 MAX VALUE 446,439.00 39.51 3.55 1.76

Relational linkage 0.50 1.00 0.99 1.00 116,947.00 0.00 -2,331.07 0.08 0.08 0.30

Tightness 0.00 0.25 0.24 0.25 1,658.62 0.00 -11,180.50 0.05 0.22 0.22

Tuples 3 1,023 23.15 3.00 161,373 MAX VALUE 9,272.01 112.47 4.86 0.22

Values 2 2 2.00 2.00 3,480 MAX VALUE 1,206.08 0.00 0.00 0.00

Value table constraints 2 54 4.89 2.00 23,100 MAX VALUE 5,416.13 7.13 1.46 1.17

Value table partitions 2 128 25.15 16.00 118,700 MAX VALUE 11,152.70 30.70 1.22 1.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	10	2.31	2.00	16,130	MAX VALUE	5,320.50	1.40	0.60	0.22
Coarse blocks size	1	512	11.14	4.00	3,096,780	MAX VALUE	446,439.00	39.51	3.55	1.76
Relational linkage	0.50	1.00	0.99	1.00	116,947.00	0.00	-2,331.07	0.08	0.08	0.30
Tightness	0.00	0.25	0.24	0.25	1,658.62	0.00	-11,180.50	0.05	0.22	0.22
Tuples	3	1,023	23.15	3.00	161,373	MAX VALUE	9,272.01	112.47	4.86	0.22
Values	2	2	2.00	2.00	3,480	MAX VALUE	1,206.08	0.00	0.00	0.00
Value table constraints	2	54	4.89	2.00	23,100	MAX VALUE	5,416.13	7.13	1.46	1.17
Value table partitions	2	128	25.15	16.00	118,700	MAX VALUE	11,152.70	30.70	1.22	1.66

Tree decomposition

Number of clusters: 1,519
Number of leaves: 101
Tree depth: 26
CIR: 0.77
Independent Cluster Pairs: 885,042
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Tree1.json

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

Cluster constraints 1 319 7.45 5.00 11,321 MAX VALUE 1,763.49 21.38 2.87 1.38

Variables per cluster 2 180 27.96 15.00 42,468 MAX VALUE 4,577.21 24.96 0.89 2.15

Separator constraints 0 215 2.86 0.00 4,350 0 None 17.41 6.08 0.58

Separator variables 0 154 26.81 14.00 40,728 0 None 24.52 0.91 2.14

Clusters per var 1 538 24.41 11.00 42,468 MAX VALUE 3,869.98 59.98 2.46 2.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	319	7.45	5.00	11,321	MAX VALUE	1,763.49	21.38	2.87	1.38
Variables per cluster	2	180	27.96	15.00	42,468	MAX VALUE	4,577.21	24.96	0.89	2.15
Separator constraints	0	215	2.86	0.00	4,350	0	None	17.41	6.08	0.58
Separator variables	0	154	26.81	14.00	40,728	0	None	24.52	0.91	2.14
Clusters per var	1	538	24.41	11.00	42,468	MAX VALUE	3,869.98	59.98	2.46	2.83

Dual tree decomposition

Number of clusters: 1,660
Number of leaves: 730
Tree depth: 16
CIR: 0.88
Independent Cluster Pairs: 1,208,010
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/DualTree1.json

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

Cluster constraints 37 3,808 517.57 336.50 859,170 MAX VALUE 8,801.29 654.92 1.27 3.29

Variables per cluster 10 343 48.10 41.50 79,840 MAX VALUE 5,591.53 55.79 1.16 2.94

Separator constraints 0 2,374 429.37 294.00 712,750 0 None 478.64 1.11 3.26

Separator variables 0 251 43.90 40.00 72,869 0 None 45.80 1.04 2.97

Clusters per variable 1 120 11.45 12.00 79,840 MAX VALUE 15,002.70 8.73 0.76 2.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	3,808	517.57	336.50	859,170	MAX VALUE	8,801.29	654.92	1.27	3.29
Variables per cluster	10	343	48.10	41.50	79,840	MAX VALUE	5,591.53	55.79	1.16	2.94
Separator constraints	0	2,374	429.37	294.00	712,750	0	None	478.64	1.11	3.26
Separator variables	0	251	43.90	40.00	72,869	0	None	45.80	1.04	2.97
Clusters per variable	1	120	11.45	12.00	79,840	MAX VALUE	15,002.70	8.73	0.76	2.82

Primal graph

Density: 0.71%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-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 1.10

Degree 1 54 12.40 10.00 21,570 MAX VALUE 4,164.43 8.47 0.68 1.50

Eccentricity 5 8 5.91 6.00 10,290 MAX VALUE 3,073.49 0.90 0.15 1.17

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	1.10
Degree	1	54	12.40	10.00	21,570	MAX VALUE	4,164.43	8.47	0.68	1.50
Eccentricity	5	8	5.91	6.00	10,290	MAX VALUE	3,073.49	0.90	0.15	1.17
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 4.19%
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 0.16 1.00 None 0.82 None None None None None 4.09

Degree 1 686 72.86 27.00 126,782 MAX VALUE 6,200.99 113.83 1.56 3.88

Eccentricity 3 5 3.57 4.00 6,205 MAX VALUE 2,191.08 0.56 0.16 0.82

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	0.16	1.00	None	0.82	None	None	None	None	None	4.09
Degree	1	686	72.86	27.00	126,782	MAX VALUE	6,200.99	113.83	1.56	3.88
Eccentricity	3	5	3.57	4.00	6,205	MAX VALUE	2,191.08	0.56	0.16	0.82
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.60%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,582,590
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.70 0.71 4,897.96 0.00 None 0.09 0.13 2.99

Degree 9 73 42.01 45.00 292,840 MAX VALUE 25,340.80 14.13 0.34 2.81

Eccentricity 5 8 6.18 6.00 43,083 MAX VALUE 12,662.70 0.62 0.10 0.89

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	0.70	0.71	4,897.96	0.00	None	0.09	0.13	2.99
Degree	9	73	42.01	45.00	292,840	MAX VALUE	25,340.80	14.13	0.34	2.81
Eccentricity	5	8	6.18	6.00	43,083	MAX VALUE	12,662.70	0.62	0.10	0.89
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 0.43 0.01 0.00 60.83 0.00 None 0.05 5.83 0.23

Degree 2 10 3.80 4.00 26,520 MAX VALUE 9,119.32 1.07 0.28 0.93

Eccentricity 13 22 17.95 18.00 125,101 MAX VALUE 20,089.50 1.87 0.10 2.01

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	60.83	0.00	None	0.05	5.83	0.23
Degree	2	10	3.80	4.00	26,520	MAX VALUE	9,119.32	1.07	0.28	0.93
Eccentricity	13	22	17.95	18.00	125,101	MAX VALUE	20,089.50	1.87	0.10	2.01
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: 0.68%

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

Clustering coefficient 0.12 1.00 0.80 0.75 5,551.64 0.00 -1,783.70 0.18 0.22 4.22

Degree 2 1,138 47.53 9.00 331,326 MAX VALUE 18,401.80 101.43 2.13 3.83

Eccentricity 4 7 5.31 5.00 37,028 MAX VALUE 11,595.00 0.60 0.11 0.90

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.12	1.00	0.80	0.75	5,551.64	0.00	-1,783.70	0.18	0.22	4.22
Degree	2	1,138	47.53	9.00	331,326	MAX VALUE	18,401.80	101.43	2.13	3.83
Eccentricity	4	7	5.31	5.00	37,028	MAX VALUE	11,595.00	0.60	0.11	0.90

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-8e2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8e2-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 54 3.70 2.00 32,260 MAX VALUE 8,351.55 5.52 1.49 0.73

Eccentricity 10 16 12.89 13.00 112,306 MAX VALUE 22,227.10 1.27 0.10 1.43

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

XCSP 2.1 Benchmarks