XCSP 2.1 Benchmark Database

Instance: normalized-ii-8b3-ext
Number of variables: 1632
Number of constraints: 6894
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 1632
Number of constraints: 6894

General features

Coarse blocks: 179,256
Value tables: 3,000

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

Arity 2 8 2.20 2.00 15,168 MAX VALUE 5,118.33 1.01 0.46 0.19

Coarse blocks size 1 128 7.30 4.00 1,309,070 MAX VALUE 251,329.00 15.32 2.10 1.69

Relational linkage 0.50 1.00 0.98 1.00 68,386.50 0.00 -2,025.64 0.10 0.10 0.33

Tightness 0.00 0.25 0.24 0.25 1,658.46 0.00 -10,513.70 0.05 0.19 0.19

Tuples 3 255 9.53 3.00 65,682 MAX VALUE 8,605.57 37.44 3.93 0.19

Values 2 2 2.00 2.00 3,264 MAX VALUE 1,131.22 0.00 0.00 0.00

Value table constraints 2 86 6.25 2.00 18,756 MAX VALUE 3,908.32 10.97 1.75 1.30

Value table partitions 2 128 23.30 2.00 69,888 MAX VALUE 6,092.76 33.63 1.44 1.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.20	2.00	15,168	MAX VALUE	5,118.33	1.01	0.46	0.19
Coarse blocks size	1	128	7.30	4.00	1,309,070	MAX VALUE	251,329.00	15.32	2.10	1.69
Relational linkage	0.50	1.00	0.98	1.00	68,386.50	0.00	-2,025.64	0.10	0.10	0.33
Tightness	0.00	0.25	0.24	0.25	1,658.46	0.00	-10,513.70	0.05	0.19	0.19
Tuples	3	255	9.53	3.00	65,682	MAX VALUE	8,605.57	37.44	3.93	0.19
Values	2	2	2.00	2.00	3,264	MAX VALUE	1,131.22	0.00	0.00	0.00
Value table constraints	2	86	6.25	2.00	18,756	MAX VALUE	3,908.32	10.97	1.75	1.30
Value table partitions	2	128	23.30	2.00	69,888	MAX VALUE	6,092.76	33.63	1.44	1.38

Tree decomposition

Number of clusters: 1,542
Number of leaves: 144
Tree depth: 16
CIR: 0.75
Independent Cluster Pairs: 890,061
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Tree1.json

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

Cluster constraints 1 43 4.77 5.00 7,360 MAX VALUE 1,737.51 4.19 0.88 1.19

Variables per cluster 2 91 19.16 14.00 29,538 MAX VALUE 4,087.16 15.17 0.79 1.76

Separator constraints 0 42 0.30 0.00 466 0 None 2.52 8.34 0.29

Separator variables 0 90 18.10 13.00 27,906 0 None 15.07 0.83 1.76

Clusters per var 1 511 18.10 7.00 29,538 MAX VALUE 2,839.27 57.67 3.19 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	43	4.77	5.00	7,360	MAX VALUE	1,737.51	4.19	0.88	1.19
Variables per cluster	2	91	19.16	14.00	29,538	MAX VALUE	4,087.16	15.17	0.79	1.76
Separator constraints	0	42	0.30	0.00	466	0	None	2.52	8.34	0.29
Separator variables	0	90	18.10	13.00	27,906	0	None	15.07	0.83	1.76
Clusters per var	1	511	18.10	7.00	29,538	MAX VALUE	2,839.27	57.67	3.19	2.29

Dual tree decomposition

Number of clusters: 1,590
Number of leaves: 738
Tree depth: 18
CIR: 0.87
Independent Cluster Pairs: 1,091,620
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/DualTree1.json

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

Cluster constraints 37 9,991 1,160.99 732.00 1,845,980 MAX VALUE 9,077.82 1,490.12 1.28 3.43

Variables per cluster 10 596 65.83 60.00 104,667 MAX VALUE 5,632.30 79.54 1.21 2.93

Separator constraints 0 5,668 1,023.47 687.00 1,627,320 0 None 1,173.81 1.15 3.41

Separator variables 0 432 61.49 59.00 97,773 0 None 67.07 1.09 2.93

Clusters per variable 1 91 15.18 17.00 104,667 MAX VALUE 16,682.20 9.06 0.60 3.07

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	9,991	1,160.99	732.00	1,845,980	MAX VALUE	9,077.82	1,490.12	1.28	3.43
Variables per cluster	10	596	65.83	60.00	104,667	MAX VALUE	5,632.30	79.54	1.21	2.93
Separator constraints	0	5,668	1,023.47	687.00	1,627,320	0	None	1,173.81	1.15	3.41
Separator variables	0	432	61.49	59.00	97,773	0	None	67.07	1.09	2.93
Clusters per variable	1	91	15.18	17.00	104,667	MAX VALUE	16,682.20	9.06	0.60	3.07

Primal graph

Density: 0.67%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Primal1.json

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

Clustering coefficient 0.00 0.79 None 0.33 None None None None None 0.95

Degree 1 86 10.95 9.00 17,868 MAX VALUE 3,482.56 13.26 1.21 1.25

Eccentricity 5 8 5.89 6.00 9,606 MAX VALUE 2,880.15 0.76 0.13 1.00

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	0.79	None	0.33	None	None	None	None	None	0.95
Degree	1	86	10.95	9.00	17,868	MAX VALUE	3,482.56	13.26	1.21	1.25
Eccentricity	5	8	5.89	6.00	9,606	MAX VALUE	2,880.15	0.76	0.13	1.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 2.40%
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 0.11 1.00 None 0.81 None None None None None 3.25

Degree 1 600 39.22 19.00 64,002 MAX VALUE 4,866.85 74.73 1.91 3.15

Eccentricity 3 5 3.97 4.00 6,472 MAX VALUE 2,222.31 0.70 0.18 1.03

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	0.11	1.00	None	0.81	None	None	None	None	None	3.25
Degree	1	600	39.22	19.00	64,002	MAX VALUE	4,866.85	74.73	1.91	3.15
Eccentricity	3	5	3.97	4.00	6,472	MAX VALUE	2,222.31	0.70	0.18	1.03
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: None%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Dual1.json

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

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	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
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 0.20 0.00 0.00 2.97 0.00 None 0.01 17.96 0.03

Degree 2 7 3.70 4.00 25,488 MAX VALUE 8,921.92 0.61 0.16 0.84

Eccentricity 18 31 24.84 25.00 171,222 MAX VALUE 22,082.40 3.32 0.13 2.51

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	0.20	0.00	0.00	2.97	0.00	None	0.01	17.96	0.03
Degree	2	7	3.70	4.00	25,488	MAX VALUE	8,921.92	0.61	0.16	0.84
Eccentricity	18	31	24.84	25.00	171,222	MAX VALUE	22,082.40	3.32	0.13	2.51
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: 1.09%

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

Clustering coefficient 0.26 1.00 0.80 0.75 5,526.03 0.00 -1,690.53 0.17 0.21 4.60

Degree 2 1,001 75.39 8.00 519,748 MAX VALUE 19,073.70 154.69 2.05 4.05

Eccentricity 4 8 5.71 6.00 39,388 MAX VALUE 11,958.70 0.72 0.13 1.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.26	1.00	0.80	0.75	5,526.03	0.00	-1,690.53	0.17	0.21	4.60
Degree	2	1,001	75.39	8.00	519,748	MAX VALUE	19,073.70	154.69	2.05	4.05
Eccentricity	4	8	5.71	6.00	39,388	MAX VALUE	11,958.70	0.72	0.13	1.09

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-8b3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b3-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 0.17

Degree 1 86 3.56 2.00 30,336 MAX VALUE 7,819.86 6.84 1.92 0.62

Eccentricity 10 16 12.80 13.00 109,174 MAX VALUE 21,706.90 1.11 0.09 1.31

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

XCSP 2.1 Benchmarks