XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-43-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 3 21 12.51 13.00 112,624 MAX VALUE 22,549.20 2.50 0.20 2.34

Relational linkage 0.12 0.56 0.36 0.36 357.24 0.00 -1,045.84 0.06 0.17 1.86

Tightness 0.44 0.54 0.50 0.50 89.90 0.00 -125.10 0.02 0.04 3.70

Tuples 286 348 312.84 313.00 56,312 MAX VALUE 1,034.10 11.98 0.04 3.70

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 5 14 9.00 9.00 360 4.13e+37 86.61 2.14 0.24 2.03

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	3	21	12.51	13.00	112,624	MAX VALUE	22,549.20	2.50	0.20	2.34
Relational linkage	0.12	0.56	0.36	0.36	357.24	0.00	-1,045.84	0.06	0.17	1.86
Tightness	0.44	0.54	0.50	0.50	89.90	0.00	-125.10	0.02	0.04	3.70
Tuples	286	348	312.84	313.00	56,312	MAX VALUE	1,034.10	11.98	0.04	3.70
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	14	9.00	9.00	360	4.13e+37	86.61	2.14	0.24	2.03
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 9
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 13
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Tree1.json

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

Cluster constraints 6 49 23.25 20.00 465 3.14e+25 58.71 14.07 0.61 2.62

Variables per cluster 6 21 12.15 10.50 243 8.87e+20 48.23 4.99 0.41 2.22

Separator constraints 0 44 14.25 10.50 285 0 None 12.89 0.90 2.69

Separator variables 0 20 10.15 9.00 203 0 None 5.12 0.50 2.29

Clusters per var 1 13 6.08 6.00 243 1.02e+25 57.59 4.15 0.68 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	49	23.25	20.00	465	3.14e+25	58.71	14.07	0.61	2.62
Variables per cluster	6	21	12.15	10.50	243	8.87e+20	48.23	4.99	0.41	2.22
Separator constraints	0	44	14.25	10.50	285	0	None	12.89	0.90	2.69
Separator variables	0	20	10.15	9.00	203	0	None	5.12	0.50	2.29
Clusters per var	1	13	6.08	6.00	243	1.02e+25	57.59	4.15	0.68	2.23

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 133
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/DualTree1.json

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

Cluster constraints 20 297 118.00 92.00 4,484 MAX VALUE 174.32 69.25 0.59 3.37

Variables per cluster 9 80 28.50 21.50 1,083 MAX VALUE 121.38 17.31 0.61 3.14

Separator constraints 0 153 77.68 70.00 2,952 0 None 40.15 0.52 3.44

Separator variables 0 58 23.76 20.00 903 0 None 13.05 0.55 3.14

Clusters per variable 1 10 6.02 7.00 1,083 MAX VALUE 292.84 2.74 0.45 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	20	297	118.00	92.00	4,484	MAX VALUE	174.32	69.25	0.59	3.37
Variables per cluster	9	80	28.50	21.50	1,083	MAX VALUE	121.38	17.31	0.61	3.14
Separator constraints	0	153	77.68	70.00	2,952	0	None	40.15	0.52	3.44
Separator variables	0	58	23.76	20.00	903	0	None	13.05	0.55	3.14
Clusters per variable	1	10	6.02	7.00	1,083	MAX VALUE	292.84	2.74	0.45	2.22

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 142
Triangles: 117
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Primal1.json

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

Clustering coefficient 0.08 0.47 0.22 0.22 8.76 0.00 -63.22 0.07 0.34 2.98

Degree 5 14 9.00 9.00 360 4.13e+37 86.61 2.14 0.24 2.03

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.28 3.00 466 MAX VALUE 167.51 0.45 0.14 0.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.08	0.47	0.22	0.22	8.76	0.00	-63.22	0.07	0.34	2.98
Degree	5	14	9.00	9.00	360	4.13e+37	86.61	2.14	0.24	2.03
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.28	3.00	466	MAX VALUE	167.51	0.45	0.14	0.59

Triangulated primal graph

Density: 52.95%
MCB compute time (ms): 7
MCB cycles: 414
Triangles: 2,521

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

Clustering coefficient 0.64 1.00 0.84 0.83 33.49 0.00 -7.46 0.11 0.13 3.13

Degree 5 32 20.65 25.00 826 MAX VALUE 114.86 9.50 0.46 2.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,242 MAX VALUE 454.82 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.84	0.83	33.49	0.00	-7.46	0.11	0.13	3.13
Degree	5	32	20.65	25.00	826	MAX VALUE	114.86	9.50	0.46	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,242	MAX VALUE	454.82	0.00	0.00	0.00

Dual graph

Density: 9.51%
MCB compute time (ms): 326
MCB cycles: 1,596
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Dual1.json

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

Clustering coefficient 0.43 0.62 0.50 0.49 89.62 0.00 -125.74 0.02 0.05 3.99

Degree 8 24 17.02 17.00 3,064 MAX VALUE 507.32 2.90 0.17 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,074 MAX VALUE 1,834.57 0.41 0.13 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.62	0.50	0.49	89.62	0.00	-125.74	0.02	0.05	3.99
Degree	8	24	17.02	17.00	3,064	MAX VALUE	507.32	2.90	0.17	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,074	MAX VALUE	1,834.57	0.41	0.13	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 73
MCB cycles: 141

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 6 3.56 3.00 640 MAX VALUE 224.31 0.75 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.72 7.00 947 MAX VALUE 266.15 1.20 0.18 1.58

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	6	3.56	3.00	640	MAX VALUE	224.31	0.75	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.72	7.00	947	MAX VALUE	266.15	1.20	0.18	1.58

Triangulated dual graph

Density: 43.87%
Triangles: 171,243

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

Clustering coefficient 0.67 1.00 0.82 0.81 148.28 0.00 -36.21 0.10 0.12 4.54

Degree 8 127 78.52 83.00 14,134 MAX VALUE 751.00 38.77 0.49 3.97

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	0.67	1.00	0.82	0.81	148.28	0.00	-36.21	0.10	0.12	4.54
Degree	8	127	78.52	83.00	14,134	MAX VALUE	751.00	38.77	0.49	3.97
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.71%

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

Clustering coefficient 0.50 1.00 0.80 0.74 143.94 0.00 -43.53 0.15 0.19 3.27

Degree 2 65 20.96 7.00 3,772 MAX VALUE 420.82 23.10 1.10 3.12

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	0.50	1.00	0.80	0.74	143.94	0.00	-43.53	0.15	0.19	3.27
Degree	2	65	20.96	7.00	3,772	MAX VALUE	420.82	23.10	1.10	3.12
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-43-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 14 3.27 2.00 720 MAX VALUE 211.38 2.85 0.87 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.55 6.00 924 MAX VALUE 263.86 0.89 0.14 0.59

XCSP 2.1 Benchmarks