XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-86-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 4 22 12.49 12.00 112,452 MAX VALUE 22,541.30 2.47 0.20 2.32

Relational linkage 0.16 0.52 0.36 0.36 358.92 0.00 -1,040.09 0.06 0.17 1.83

Tightness 0.45 0.55 0.50 0.50 90.04 0.00 -124.83 0.02 0.04 3.77

Tuples 280 344 312.37 312.00 56,226 MAX VALUE 1,033.82 12.13 0.04 3.77

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

Value table constraints 4 15 9.00 9.00 360 1.97e+37 85.87 2.71 0.30 2.32

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	4	22	12.49	12.00	112,452	MAX VALUE	22,541.30	2.47	0.20	2.32
Relational linkage	0.16	0.52	0.36	0.36	358.92	0.00	-1,040.09	0.06	0.17	1.83
Tightness	0.45	0.55	0.50	0.50	90.04	0.00	-124.83	0.02	0.04	3.77
Tuples	280	344	312.37	312.00	56,226	MAX VALUE	1,033.82	12.13	0.04	3.77
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.00	9.00	360	1.97e+37	85.87	2.71	0.30	2.32
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: 21
Number of leaves: 11
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 16
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Tree1.json

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

Cluster constraints 6 53 22.14 17.00 465 9.20e+25 59.78 14.87 0.67 2.76

Variables per cluster 5 20 11.14 11.00 234 1.14e+21 48.49 4.91 0.44 2.40

Separator constraints 0 42 13.57 8.00 285 0 None 13.07 0.96 2.57

Separator variables 0 18 9.24 7.00 194 0 None 4.95 0.54 2.40

Clusters per var 1 15 5.85 6.50 234 8.85e+23 55.14 4.22 0.72 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	53	22.14	17.00	465	9.20e+25	59.78	14.87	0.67	2.76
Variables per cluster	5	20	11.14	11.00	234	1.14e+21	48.49	4.91	0.44	2.40
Separator constraints	0	42	13.57	8.00	285	0	None	13.07	0.96	2.57
Separator variables	0	18	9.24	7.00	194	0	None	4.95	0.54	2.40
Clusters per var	1	15	5.85	6.50	234	8.85e+23	55.14	4.22	0.72	2.23

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 135
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/DualTree1.json

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

Cluster constraints 31 369 125.34 102.00 4,763 MAX VALUE 175.48 84.07 0.67 3.60

Variables per cluster 11 81 28.89 22.00 1,098 MAX VALUE 121.47 18.33 0.63 3.12

Separator constraints 0 198 83.58 69.50 3,176 0 None 50.23 0.60 3.49

Separator variables 0 62 24.16 20.50 918 0 None 13.96 0.58 3.14

Clusters per variable 1 11 6.10 7.00 1,098 MAX VALUE 295.96 2.72 0.45 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	31	369	125.34	102.00	4,763	MAX VALUE	175.48	84.07	0.67	3.60
Variables per cluster	11	81	28.89	22.00	1,098	MAX VALUE	121.47	18.33	0.63	3.12
Separator constraints	0	198	83.58	69.50	3,176	0	None	50.23	0.60	3.49
Separator variables	0	62	24.16	20.50	918	0	None	13.96	0.58	3.14
Clusters per variable	1	11	6.10	7.00	1,098	MAX VALUE	295.96	2.72	0.45	2.26

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 161
Triangles: 123
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Primal1.json

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

Clustering coefficient 0.10 0.40 0.23 0.20 9.36 0.00 -60.56 0.08 0.34 3.09

Degree 4 15 9.00 9.00 360 1.97e+37 85.87 2.71 0.30 2.32

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.34 3.00 537 MAX VALUE 192.41 0.47 0.14 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.40	0.23	0.20	9.36	0.00	-60.56	0.08	0.34	3.09
Degree	4	15	9.00	9.00	360	1.97e+37	85.87	2.71	0.30	2.32
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.34	3.00	537	MAX VALUE	192.41	0.47	0.14	0.64

Triangulated primal graph

Density: 49.23%
MCB compute time (ms): 9
MCB cycles: 361
Triangles: 2,196

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

Clustering coefficient 0.60 1.00 0.84 0.81 33.41 0.00 -7.64 0.12 0.15 2.99

Degree 4 33 19.20 24.50 768 MAX VALUE 110.69 9.55 0.50 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,083 MAX VALUE 396.60 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.60	1.00	0.84	0.81	33.41	0.00	-7.64	0.12	0.15	2.99
Degree	4	33	19.20	24.50	768	MAX VALUE	110.69	9.55	0.50	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,083	MAX VALUE	396.60	0.00	0.00	0.00

Dual graph

Density: 9.85%
MCB compute time (ms): 276
MCB cycles: 1,809
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Dual1.json

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

Clustering coefficient 0.45 0.67 0.51 0.50 92.00 0.00 -121.29 0.04 0.08 4.36

Degree 10 26 17.63 18.00 3,174 MAX VALUE 512.77 3.56 0.20 2.64

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.24 3.00 5,860 MAX VALUE 2,109.25 0.48 0.15 0.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.67	0.51	0.50	92.00	0.00	-121.29	0.04	0.08	4.36
Degree	10	26	17.63	18.00	3,174	MAX VALUE	512.77	3.56	0.20	2.64
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.24	3.00	5,860	MAX VALUE	2,109.25	0.48	0.15	0.60

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 82
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.43 0.00 None 0.02 7.86 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 225.01 0.68 0.19 1.02

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.79 7.00 958 MAX VALUE 268.23 1.06 0.16 1.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.43	0.00	None	0.02	7.86	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	225.01	0.68	0.19	1.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.79	7.00	958	MAX VALUE	268.23	1.06	0.16	1.43

Triangulated dual graph

Density: 45.71%
Triangles: 188,208

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

Clustering coefficient 0.66 1.00 0.83 0.81 149.33 0.00 -34.75 0.09 0.11 4.58

Degree 10 136 81.82 93.00 14,728 MAX VALUE 758.02 39.77 0.49 4.11

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	0.66	1.00	0.83	0.81	149.33	0.00	-34.75	0.09	0.11	4.58
Degree	10	136	81.82	93.00	14,728	MAX VALUE	758.02	39.77	0.49	4.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.81%

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

Clustering coefficient 0.53 1.00 0.80 0.75 144.43 0.00 -43.21 0.16 0.20 3.24

Degree 2 68 21.14 7.00 3,806 MAX VALUE 424.07 22.98 1.09 3.11

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	0.53	1.00	0.80	0.75	144.43	0.00	-43.21	0.16	0.20	3.24
Degree	2	68	21.14	7.00	3,806	MAX VALUE	424.07	22.98	1.09	3.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 45
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-86-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 15 3.27 2.00 720 MAX VALUE 210.64 2.94 0.90 0.90

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.50 6.00 916 MAX VALUE 262.71 0.86 0.13 0.56

XCSP 2.1 Benchmarks