XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-63-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 12.47 12.00 112,244 MAX VALUE 22,519.10 2.49 0.20 2.33

Relational linkage 0.12 0.56 0.36 0.36 355.04 0.00 -1,051.80 0.06 0.17 1.85

Tightness 0.43 0.56 0.50 0.50 90.20 0.00 -124.52 0.02 0.04 3.79

Tuples 277 357 311.79 312.00 56,122 MAX VALUE 1,033.45 13.38 0.04 3.79

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 2.62e+37 86.16 2.52 0.28 2.26

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	12.47	12.00	112,244	MAX VALUE	22,519.10	2.49	0.20	2.33
Relational linkage	0.12	0.56	0.36	0.36	355.04	0.00	-1,051.80	0.06	0.17	1.85
Tightness	0.43	0.56	0.50	0.50	90.20	0.00	-124.52	0.02	0.04	3.79
Tuples	277	357	311.79	312.00	56,122	MAX VALUE	1,033.45	13.38	0.04	3.79
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	2.62e+37	86.16	2.52	0.28	2.26
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: 0.07
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Tree1.json

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

Cluster constraints 6 49 22.14 18.00 465 1.64e+26 60.36 14.32 0.65 2.76

Variables per cluster 5 20 11.33 11.00 238 1.74e+21 48.91 5.00 0.44 2.27

Separator constraints 0 44 13.57 10.00 285 0 None 12.97 0.96 2.46

Separator variables 0 19 9.43 8.00 198 0 None 5.07 0.54 2.36

Clusters per var 1 12 5.95 6.50 238 2.66e+24 56.24 4.13 0.69 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	49	22.14	18.00	465	1.64e+26	60.36	14.32	0.65	2.76
Variables per cluster	5	20	11.33	11.00	238	1.74e+21	48.91	5.00	0.44	2.27
Separator constraints	0	44	13.57	10.00	285	0	None	12.97	0.96	2.46
Separator variables	0	19	9.43	8.00	198	0	None	5.07	0.54	2.36
Clusters per var	1	12	5.95	6.50	238	2.66e+24	56.24	4.13	0.69	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 136
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/DualTree1.json

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

Cluster constraints 31 367 123.95 103.00 4,710 MAX VALUE 174.94 85.31 0.69 3.49

Variables per cluster 11 86 28.66 22.00 1,089 MAX VALUE 121.24 18.34 0.64 3.04

Separator constraints 0 191 82.71 71.00 3,143 0 None 52.39 0.63 3.51

Separator variables 0 61 23.92 19.00 909 0 None 13.93 0.58 2.99

Clusters per variable 1 10 6.05 7.00 1,089 MAX VALUE 294.69 2.68 0.44 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	31	367	123.95	103.00	4,710	MAX VALUE	174.94	85.31	0.69	3.49
Variables per cluster	11	86	28.66	22.00	1,089	MAX VALUE	121.24	18.34	0.64	3.04
Separator constraints	0	191	82.71	71.00	3,143	0	None	52.39	0.63	3.51
Separator variables	0	61	23.92	19.00	909	0	None	13.93	0.58	2.99
Clusters per variable	1	10	6.05	7.00	1,089	MAX VALUE	294.69	2.68	0.44	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 162
Triangles: 127
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Primal1.json

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

Clustering coefficient 0.10 0.50 0.25 0.25 10.12 0.00 -57.12 0.08 0.31 3.14

Degree 4 14 9.00 9.00 360 2.62e+37 86.16 2.52 0.28 2.26

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.28 3.00 532 MAX VALUE 191.21 0.45 0.14 0.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.50	0.25	0.25	10.12	0.00	-57.12	0.08	0.31	3.14
Degree	4	14	9.00	9.00	360	2.62e+37	86.16	2.52	0.28	2.26
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.28	3.00	532	MAX VALUE	191.21	0.45	0.14	0.60

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 6
MCB cycles: 424
Triangles: 2,244

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

Clustering coefficient 0.65 1.00 0.83 0.81 33.38 0.00 -7.64 0.12 0.14 2.99

Degree 4 30 19.40 24.50 776 MAX VALUE 111.42 9.47 0.49 2.81

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,272 MAX VALUE 465.81 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.83	0.81	33.38	0.00	-7.64	0.12	0.14	2.99
Degree	4	30	19.40	24.50	776	MAX VALUE	111.42	9.47	0.49	2.81
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,272	MAX VALUE	465.81	0.00	0.00	0.00

Dual graph

Density: 9.73%
MCB compute time (ms): 346
MCB cycles: 1,675
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Dual1.json

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

Clustering coefficient 0.46 0.66 0.51 0.50 91.52 0.00 -122.14 0.04 0.07 4.18

Degree 10 25 17.41 17.50 3,134 MAX VALUE 510.91 3.30 0.19 2.57

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.19 3.00 5,335 MAX VALUE 1,929.03 0.40 0.12 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.66	0.51	0.50	91.52	0.00	-122.14	0.04	0.07	4.18
Degree	10	25	17.41	17.50	3,134	MAX VALUE	510.91	3.30	0.19	2.57
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.19	3.00	5,335	MAX VALUE	1,929.03	0.40	0.12	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 95
MCB cycles: 141

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

Clustering coefficient 0.00 1.00 0.01 0.00 1.87 0.00 None 0.08 7.77 0.19

Degree 2 5 3.56 3.00 640 MAX VALUE 224.65 0.72 0.20 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.82 7.00 962 MAX VALUE 268.59 1.12 0.16 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.01	0.00	1.87	0.00	None	0.08	7.77	0.19
Degree	2	5	3.56	3.00	640	MAX VALUE	224.65	0.72	0.20	1.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.82	7.00	962	MAX VALUE	268.59	1.12	0.16	1.48

Triangulated dual graph

Density: 45.61%
Triangles: 191,219

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

Clustering coefficient 0.70 1.00 0.83 0.81 149.88 0.00 -33.91 0.09 0.10 4.60

Degree 10 128 81.63 95.00 14,694 MAX VALUE 755.78 40.61 0.50 3.91

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	0.70	1.00	0.83	0.81	149.88	0.00	-33.91	0.09	0.10	4.60
Degree	10	128	81.63	95.00	14,694	MAX VALUE	755.78	40.61	0.50	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.49%

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

Clustering coefficient 0.48 1.00 0.80 0.75 144.38 0.00 -42.89 0.15 0.19 3.36

Degree 2 67 22.36 7.00 4,024 MAX VALUE 432.44 24.16 1.08 3.09

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	0.48	1.00	0.80	0.75	144.38	0.00	-42.89	0.15	0.19	3.36
Degree	2	67	22.36	7.00	4,024	MAX VALUE	432.44	24.16	1.08	3.09
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-2-40-25-180-500-63-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-63-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 210.93 2.91 0.89 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.37 6.00 898 MAX VALUE 260.12 0.78 0.12 0.48

XCSP 2.1 Benchmarks