XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-70-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:29
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 12.50 12.00 112,482 MAX VALUE 22,541.30 2.48 0.20 2.33

Relational linkage 0.16 0.52 0.36 0.36 355.80 0.00 -1,048.51 0.06 0.17 1.81

Tightness 0.44 0.55 0.50 0.50 90.01 0.00 -124.86 0.02 0.04 3.65

Tuples 281 347 312.45 312.00 56,241 MAX VALUE 1,033.87 11.68 0.04 3.65

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

Value table constraints 4 14 9.00 9.00 360 1.94e+37 85.86 2.68 0.30 2.21

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	12.50	12.00	112,482	MAX VALUE	22,541.30	2.48	0.20	2.33
Relational linkage	0.16	0.52	0.36	0.36	355.80	0.00	-1,048.51	0.06	0.17	1.81
Tightness	0.44	0.55	0.50	0.50	90.01	0.00	-124.86	0.02	0.04	3.65
Tuples	281	347	312.45	312.00	56,241	MAX VALUE	1,033.87	11.68	0.04	3.65
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	9.00	360	1.94e+37	85.86	2.68	0.30	2.21
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: 0.12
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Tree1.json

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

Cluster constraints 4 51 21.05 15.00 442 1.43e+25 57.92 15.59 0.74 2.82

Variables per cluster 5 20 11.05 9.00 232 9.12e+20 48.26 5.00 0.45 2.38

Separator constraints 0 43 12.48 7.00 262 0 None 13.50 1.08 2.56

Separator variables 0 19 9.14 8.00 192 0 None 5.02 0.55 2.44

Clusters per var 1 14 5.80 6.50 232 8.94e+23 55.15 4.06 0.70 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	51	21.05	15.00	442	1.43e+25	57.92	15.59	0.74	2.82
Variables per cluster	5	20	11.05	9.00	232	9.12e+20	48.26	5.00	0.45	2.38
Separator constraints	0	43	12.48	7.00	262	0	None	13.50	1.08	2.56
Separator variables	0	19	9.14	8.00	192	0	None	5.02	0.55	2.44
Clusters per var	1	14	5.80	6.50	232	8.94e+23	55.15	4.06	0.70	2.25

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 137
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/DualTree1.json

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

Cluster constraints 31 414 128.68 96.00 4,890 MAX VALUE 175.61 93.34 0.73 3.53

Variables per cluster 11 90 29.50 22.00 1,121 MAX VALUE 121.77 19.79 0.67 2.96

Separator constraints 0 240 87.00 71.50 3,306 0 None 56.39 0.65 3.60

Separator variables 0 68 24.76 20.50 941 0 None 15.17 0.61 3.12

Clusters per variable 1 11 6.23 7.00 1,121 MAX VALUE 300.12 2.70 0.43 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	31	414	128.68	96.00	4,890	MAX VALUE	175.61	93.34	0.73	3.53
Variables per cluster	11	90	29.50	22.00	1,121	MAX VALUE	121.77	19.79	0.67	2.96
Separator constraints	0	240	87.00	71.50	3,306	0	None	56.39	0.65	3.60
Separator variables	0	68	24.76	20.50	941	0	None	15.17	0.61	3.12
Clusters per variable	1	11	6.23	7.00	1,121	MAX VALUE	300.12	2.70	0.43	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 158
Triangles: 106
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Primal1.json

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

Clustering coefficient 0.00 0.36 0.20 0.20 7.99 0.00 None 0.08 0.38 3.27

Degree 4 14 9.00 9.00 360 1.94e+37 85.86 2.68 0.30 2.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.39 3.00 536 MAX VALUE 191.42 0.49 0.14 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.36	0.20	0.20	7.99	0.00	None	0.08	0.38	3.27
Degree	4	14	9.00	9.00	360	1.94e+37	85.86	2.68	0.30	2.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.39	3.00	536	MAX VALUE	191.42	0.49	0.14	0.67

Triangulated primal graph

Density: 48.97%
MCB compute time (ms): 6
MCB cycles: 400
Triangles: 2,186

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

Clustering coefficient 0.63 1.00 0.84 0.81 33.41 0.00 -7.60 0.12 0.14 2.96

Degree 4 32 19.10 24.50 764 MAX VALUE 110.41 9.54 0.50 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,200 MAX VALUE 439.44 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.84	0.81	33.41	0.00	-7.60	0.12	0.14	2.96
Degree	4	32	19.10	24.50	764	MAX VALUE	110.41	9.54	0.50	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,200	MAX VALUE	439.44	0.00	0.00	0.00

Dual graph

Density: 9.83%
MCB compute time (ms): 222
MCB cycles: 2,023
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Dual1.json

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

Clustering coefficient 0.44 0.68 0.51 0.50 91.60 0.00 -122.12 0.04 0.08 4.25

Degree 10 25 17.60 18.00 3,168 MAX VALUE 512.67 3.39 0.19 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.35 3.00 6,783 MAX VALUE 2,423.90 0.54 0.16 0.73

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.68	0.51	0.50	91.60	0.00	-122.12	0.04	0.08	4.25
Degree	10	25	17.60	18.00	3,168	MAX VALUE	512.67	3.39	0.19	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.35	3.00	6,783	MAX VALUE	2,423.90	0.54	0.16	0.73

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 76
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 3.00 640 MAX VALUE 224.46 0.74 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.78 7.00 956 MAX VALUE 267.73 1.12 0.17 1.49

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	3.00	640	MAX VALUE	224.46	0.74	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.78	7.00	956	MAX VALUE	267.73	1.12	0.17	1.49

Triangulated dual graph

Density: 48.81%
Triangles: 219,998

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

Clustering coefficient 0.71 1.00 0.84 0.82 151.50 0.00 -31.85 0.08 0.10 4.67

Degree 10 136 87.37 105.00 15,726 MAX VALUE 768.89 41.89 0.48 4.03

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	0.71	1.00	0.84	0.82	151.50	0.00	-31.85	0.08	0.10	4.67
Degree	10	136	87.37	105.00	15,726	MAX VALUE	768.89	41.89	0.48	4.03
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 0.53 1.00 0.80 0.74 143.75 0.00 -43.93 0.16 0.20 3.34

Degree 2 65 21.10 7.00 3,798 MAX VALUE 423.68 23.02 1.09 3.15

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	0.74	143.75	0.00	-43.93	0.16	0.20	3.34
Degree	2	65	21.10	7.00	3,798	MAX VALUE	423.68	23.02	1.09	3.15
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-70-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 210.62 2.93 0.90 0.88

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.64 6.00 936 MAX VALUE 265.58 0.93 0.14 0.63

XCSP 2.1 Benchmarks