XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-38-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 21 12.48 12.00 112,348 MAX VALUE 22,524.50 2.51 0.20 2.34

Relational linkage 0.16 0.56 0.35 0.36 351.92 0.00 -1,060.69 0.06 0.18 1.85

Tightness 0.46 0.56 0.50 0.50 90.12 0.00 -124.64 0.02 0.04 3.70

Tuples 276 340 312.08 313.00 56,174 MAX VALUE 1,033.66 11.49 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 13 9.00 9.00 360 4.28e+37 86.65 2.13 0.24 2.10

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	21	12.48	12.00	112,348	MAX VALUE	22,524.50	2.51	0.20	2.34
Relational linkage	0.16	0.56	0.35	0.36	351.92	0.00	-1,060.69	0.06	0.18	1.85
Tightness	0.46	0.56	0.50	0.50	90.12	0.00	-124.64	0.02	0.04	3.70
Tuples	276	340	312.08	313.00	56,174	MAX VALUE	1,033.66	11.49	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	13	9.00	9.00	360	4.28e+37	86.65	2.13	0.24	2.10
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: 5
CIR: 0.11
Independent Cluster Pairs: 20
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Tree1.json

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

Cluster constraints 7 49 21.76 18.00 457 3.14e+26 61.01 13.11 0.60 2.85

Variables per cluster 6 19 11.33 11.00 238 2.61e+21 49.31 4.52 0.40 2.27

Separator constraints 0 39 13.19 8.00 277 0 None 12.07 0.92 2.85

Separator variables 0 17 9.43 8.00 198 0 None 4.60 0.49 2.24

Clusters per var 1 14 5.95 6.00 238 2.79e+24 56.29 4.12 0.69 2.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	49	21.76	18.00	457	3.14e+26	61.01	13.11	0.60	2.85
Variables per cluster	6	19	11.33	11.00	238	2.61e+21	49.31	4.52	0.40	2.27
Separator constraints	0	39	13.19	8.00	277	0	None	12.07	0.92	2.85
Separator variables	0	17	9.43	8.00	198	0	None	4.60	0.49	2.24
Clusters per var	1	14	5.95	6.00	238	2.79e+24	56.29	4.12	0.69	2.30

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 134
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/DualTree1.json

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

Cluster constraints 33 303 117.89 108.50 4,480 MAX VALUE 175.24 66.67 0.57 3.49

Variables per cluster 11 81 28.47 21.50 1,082 MAX VALUE 121.54 17.28 0.61 3.18

Separator constraints 0 161 77.61 77.50 2,949 0 None 38.31 0.49 3.53

Separator variables 0 59 23.74 20.00 902 0 None 13.04 0.55 3.06

Clusters per variable 1 11 6.01 7.00 1,082 MAX VALUE 292.35 2.74 0.46 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	33	303	117.89	108.50	4,480	MAX VALUE	175.24	66.67	0.57	3.49
Variables per cluster	11	81	28.47	21.50	1,082	MAX VALUE	121.54	17.28	0.61	3.18
Separator constraints	0	161	77.61	77.50	2,949	0	None	38.31	0.49	3.53
Separator variables	0	59	23.74	20.00	902	0	None	13.04	0.55	3.06
Clusters per variable	1	11	6.01	7.00	1,082	MAX VALUE	292.35	2.74	0.46	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 145
Triangles: 112
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Primal1.json

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

Clustering coefficient 0.13 0.50 0.23 0.23 9.31 0.00 -59.75 0.07 0.28 2.95

Degree 5 13 9.00 9.00 360 4.28e+37 86.65 2.13 0.24 2.10

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.27 3.00 474 MAX VALUE 170.52 0.44 0.14 0.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.13	0.50	0.23	0.23	9.31	0.00	-59.75	0.07	0.28	2.95
Degree	5	13	9.00	9.00	360	4.28e+37	86.65	2.13	0.24	2.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.27	3.00	474	MAX VALUE	170.52	0.44	0.14	0.58

Triangulated primal graph

Density: 49.62%
MCB compute time (ms): 18
MCB cycles: 348
Triangles: 2,179

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

Clustering coefficient 0.61 1.00 0.83 0.81 33.14 0.00 -7.97 0.12 0.15 2.99

Degree 5 32 19.35 23.50 774 MAX VALUE 111.90 9.24 0.48 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,044 MAX VALUE 382.32 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.61	1.00	0.83	0.81	33.14	0.00	-7.97	0.12	0.15	2.99
Degree	5	32	19.35	23.50	774	MAX VALUE	111.90	9.24	0.48	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,044	MAX VALUE	382.32	0.00	0.00	0.00

Dual graph

Density: 9.50%
MCB compute time (ms): 485
MCB cycles: 1,476
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Dual1.json

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

Clustering coefficient 0.45 0.61 0.50 0.49 90.00 0.00 -124.97 0.02 0.05 3.91

Degree 10 24 17.01 17.00 3,062 MAX VALUE 507.46 2.83 0.17 2.41

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.11 3.00 4,587 MAX VALUE 1,667.10 0.32 0.10 0.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.61	0.50	0.49	90.00	0.00	-124.97	0.02	0.05	3.91
Degree	10	24	17.01	17.00	3,062	MAX VALUE	507.46	2.83	0.17	2.41
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.11	3.00	4,587	MAX VALUE	1,667.10	0.32	0.10	0.35

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 5 3.56 4.00 640 MAX VALUE 224.73 0.70 0.20 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.65 7.00 937 MAX VALUE 264.54 1.19 0.18 1.52

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	5	3.56	4.00	640	MAX VALUE	224.73	0.70	0.20	1.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.65	7.00	937	MAX VALUE	264.54	1.19	0.18	1.52

Triangulated dual graph

Density: 43.77%
Triangles: 172,643

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

Clustering coefficient 0.67 1.00 0.83 0.79 148.54 0.00 -35.77 0.10 0.12 4.67

Degree 10 127 78.34 92.00 14,102 MAX VALUE 749.47 39.30 0.50 3.89

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	0.83	0.79	148.54	0.00	-35.77	0.10	0.12	4.67
Degree	10	127	78.34	92.00	14,102	MAX VALUE	749.47	39.30	0.50	3.89
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.79%

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

Clustering coefficient 0.47 1.00 0.80 0.75 143.78 0.00 -43.70 0.15 0.19 3.28

Degree 2 64 21.11 7.00 3,800 MAX VALUE 423.60 23.15 1.10 3.01

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	0.47	1.00	0.80	0.75	143.78	0.00	-43.70	0.15	0.19	3.28
Degree	2	64	21.11	7.00	3,800	MAX VALUE	423.60	23.15	1.10	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 37
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-38-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 13 3.27 2.00 720 MAX VALUE 211.42 2.85 0.87 0.86

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