XCSP 2.1 Benchmark Database

Instance: normalized-ii-8b2-ext
Number of variables: 1152
Number of constraints: 4652
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 1152
Number of constraints: 4652

General features

Coarse blocks: 97,080
Value tables: 1,950

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

Arity 2 8 2.21 2.00 10,272 MAX VALUE 3,462.13 1.03 0.47 0.20

Coarse blocks size 1 128 7.68 4.00 745,488 MAX VALUE 133,630.00 17.29 2.25 1.72

Relational linkage 0.50 1.00 0.97 1.00 37,433.10 0.00 -1,374.13 0.11 0.11 0.38

Tightness 0.00 0.25 0.24 0.25 1,117.67 0.00 -7,120.01 0.05 0.20 0.20

Tuples 3 255 9.88 3.00 45,972 MAX VALUE 5,834.11 38.59 3.90 0.20

Values 2 2 2.00 2.00 2,304 MAX VALUE 798.51 0.00 0.00 0.00

Value table constraints 2 56 6.20 2.00 12,096 MAX VALUE 2,574.11 8.99 1.45 1.23

Value table partitions 2 128 19.72 2.00 38,448 MAX VALUE 3,626.55 30.84 1.56 1.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.21	2.00	10,272	MAX VALUE	3,462.13	1.03	0.47	0.20
Coarse blocks size	1	128	7.68	4.00	745,488	MAX VALUE	133,630.00	17.29	2.25	1.72
Relational linkage	0.50	1.00	0.97	1.00	37,433.10	0.00	-1,374.13	0.11	0.11	0.38
Tightness	0.00	0.25	0.24	0.25	1,117.67	0.00	-7,120.01	0.05	0.20	0.20
Tuples	3	255	9.88	3.00	45,972	MAX VALUE	5,834.11	38.59	3.90	0.20
Values	2	2	2.00	2.00	2,304	MAX VALUE	798.51	0.00	0.00	0.00
Value table constraints	2	56	6.20	2.00	12,096	MAX VALUE	2,574.11	8.99	1.45	1.23
Value table partitions	2	128	19.72	2.00	38,448	MAX VALUE	3,626.55	30.84	1.56	1.32

Tree decomposition

Number of clusters: 1,062
Number of leaves: 104
Tree depth: 16
CIR: 0.75
Independent Cluster Pairs: 420,706
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Tree1.json

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

Cluster constraints 1 43 4.82 5.00 5,118 MAX VALUE 1,207.09 4.43 0.92 1.28

Variables per cluster 2 91 19.11 14.00 20,298 MAX VALUE 2,812.12 15.30 0.80 1.81

Separator constraints 0 42 0.44 0.00 466 0 None 3.03 6.90 0.40

Separator variables 0 90 18.03 13.00 19,146 0 None 15.15 0.84 1.81

Clusters per var 1 331 17.62 7.00 20,298 MAX VALUE 2,074.64 45.79 2.60 2.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	43	4.82	5.00	5,118	MAX VALUE	1,207.09	4.43	0.92	1.28
Variables per cluster	2	91	19.11	14.00	20,298	MAX VALUE	2,812.12	15.30	0.80	1.81
Separator constraints	0	42	0.44	0.00	466	0	None	3.03	6.90	0.40
Separator variables	0	90	18.03	13.00	19,146	0	None	15.15	0.84	1.81
Clusters per var	1	331	17.62	7.00	20,298	MAX VALUE	2,074.64	45.79	2.60	2.47

Dual tree decomposition

Number of clusters: 1,110
Number of leaves: 498
Tree depth: 14
CIR: 0.85
Independent Cluster Pairs: 521,544
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/DualTree1.json

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

Cluster constraints 37 5,135 607.25 452.00 674,051 MAX VALUE 5,971.45 763.63 1.26 3.37

Variables per cluster 10 399 51.16 44.00 56,782 MAX VALUE 3,772.73 60.55 1.18 2.91

Separator constraints 0 2,749 512.42 404.00 568,787 0 None 565.71 1.10 3.35

Separator variables 0 307 46.96 43.00 52,130 0 None 50.00 1.06 2.90

Clusters per variable 1 73 12.21 13.00 56,782 MAX VALUE 10,335.50 7.46 0.61 2.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	5,135	607.25	452.00	674,051	MAX VALUE	5,971.45	763.63	1.26	3.37
Variables per cluster	10	399	51.16	44.00	56,782	MAX VALUE	3,772.73	60.55	1.18	2.91
Separator constraints	0	2,749	512.42	404.00	568,787	0	None	565.71	1.10	3.35
Separator variables	0	307	46.96	43.00	52,130	0	None	50.00	1.06	2.90
Clusters per variable	1	73	12.21	13.00	56,782	MAX VALUE	10,335.50	7.46	0.61	2.88

Primal graph

Density: 0.93%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-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 1.03

Degree 1 56 10.72 9.00 12,348 MAX VALUE 2,488.07 9.94 0.93 1.41

Eccentricity 5 8 5.96 6.00 6,864 MAX VALUE 2,045.26 0.84 0.14 1.11

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	1.03
Degree	1	56	10.72	9.00	12,348	MAX VALUE	2,488.07	9.94	0.93	1.41
Eccentricity	5	8	5.96	6.00	6,864	MAX VALUE	2,045.26	0.84	0.14	1.11
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 3.51%
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 0.81 None None None None None 3.44

Degree 1 420 40.35 19.00 46,482 MAX VALUE 3,487.03 65.92 1.63 3.30

Eccentricity 3 5 3.91 4.00 4,505 MAX VALUE 1,552.54 0.69 0.18 1.02

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	0.81	None	None	None	None	None	3.44
Degree	1	420	40.35	19.00	46,482	MAX VALUE	3,487.03	65.92	1.63	3.30
Eccentricity	3	5	3.91	4.00	4,505	MAX VALUE	1,552.54	0.69	0.18	1.02
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.97%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,277,510
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.71 0.73 3,325.26 0.00 None 0.11 0.15 2.75

Degree 6 82 45.26 51.00 210,528 MAX VALUE 17,151.50 16.15 0.36 2.67

Eccentricity 5 8 6.04 6.00 28,096 MAX VALUE 8,351.04 0.49 0.08 0.64

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	0.73	3,325.26	0.00	None	0.11	0.15	2.75
Degree	6	82	45.26	51.00	210,528	MAX VALUE	17,151.50	16.15	0.36	2.67
Eccentricity	5	8	6.04	6.00	28,096	MAX VALUE	8,351.04	0.49	0.08	0.64
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.08%
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 0.40 0.00 0.00 13.00 0.00 None 0.03 9.65 0.09

Degree 2 6 3.68 4.00 17,136 MAX VALUE 5,999.33 0.63 0.17 0.86

Eccentricity 14 24 19.78 20.00 92,028 MAX VALUE 13,850.70 2.38 0.12 2.22

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	0.40	0.00	0.00	13.00	0.00	None	0.03	9.65	0.09
Degree	2	6	3.68	4.00	17,136	MAX VALUE	5,999.33	0.63	0.17	0.86
Eccentricity	14	24	19.78	20.00	92,028	MAX VALUE	13,850.70	2.38	0.12	2.22
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: 1.23%

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

Clustering coefficient 0.24 1.00 0.80 0.75 3,707.67 0.00 -1,176.38 0.18 0.22 4.45

Degree 2 766 57.30 7.00 266,552 MAX VALUE 12,540.20 109.12 1.90 3.95

Eccentricity 4 7 5.23 5.00 24,330 MAX VALUE 7,663.53 0.61 0.12 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.24	1.00	0.80	0.75	3,707.67	0.00	-1,176.38	0.18	0.22	4.45
Degree	2	766	57.30	7.00	266,552	MAX VALUE	12,540.20	109.12	1.90	3.95
Eccentricity	4	7	5.23	5.00	24,330	MAX VALUE	7,663.53	0.61	0.12	0.93

Incidence graph

Density: 0.06%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b2-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 0.23

Degree 1 56 3.54 2.00 20,544 MAX VALUE 5,406.83 5.61 1.59 0.67

Eccentricity 10 16 12.75 13.00 74,024 MAX VALUE 14,751.90 1.15 0.09 1.25

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

XCSP 2.1 Benchmarks