XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-96-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 2 22 12.43 12.00 111,868 MAX VALUE 22,483.30 2.52 0.20 2.34

Relational linkage 0.08 0.52 0.35 0.36 351.36 0.00 -1,061.96 0.06 0.17 1.81

Tightness 0.44 0.55 0.50 0.50 90.51 0.00 -123.91 0.02 0.04 3.78

Tuples 281 348 310.74 309.50 55,934 MAX VALUE 1,032.87 12.68 0.04 3.78

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 4.79e+37 86.76 2.09 0.23 2.05

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	2	22	12.43	12.00	111,868	MAX VALUE	22,483.30	2.52	0.20	2.34
Relational linkage	0.08	0.52	0.35	0.36	351.36	0.00	-1,061.96	0.06	0.17	1.81
Tightness	0.44	0.55	0.50	0.50	90.51	0.00	-123.91	0.02	0.04	3.78
Tuples	281	348	310.74	309.50	55,934	MAX VALUE	1,032.87	12.68	0.04	3.78
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	4.79e+37	86.76	2.09	0.23	2.05
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: 12
Tree depth: 4
CIR: 0.07
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Tree1.json

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

Cluster constraints 7 48 20.86 15.00 438 9.77e+25 59.84 12.79 0.61 2.69

Variables per cluster 6 20 11.62 9.00 244 4.37e+21 49.83 4.73 0.41 2.24

Separator constraints 0 41 12.29 6.00 258 0 None 11.93 0.97 2.62

Separator variables 0 19 9.71 8.00 204 0 None 4.85 0.50 2.31

Clusters per var 1 14 6.10 6.50 244 1.94e+24 55.92 4.40 0.72 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	48	20.86	15.00	438	9.77e+25	59.84	12.79	0.61	2.69
Variables per cluster	6	20	11.62	9.00	244	4.37e+21	49.83	4.73	0.41	2.24
Separator constraints	0	41	12.29	6.00	258	0	None	11.93	0.97	2.62
Separator variables	0	19	9.71	8.00	204	0	None	4.85	0.50	2.31
Clusters per var	1	14	6.10	6.50	244	1.94e+24	55.92	4.40	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-2-40-25-180-500-96-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/DualTree1.json

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

Cluster constraints 25 322 119.24 105.00 4,531 MAX VALUE 175.03 72.52 0.61 3.39

Variables per cluster 10 82 28.82 23.00 1,095 MAX VALUE 121.78 17.94 0.62 3.03

Separator constraints 0 191 79.05 73.00 3,004 0 None 43.87 0.55 3.27

Separator variables 0 63 24.08 21.00 915 0 None 13.61 0.57 3.15

Clusters per variable 1 10 6.08 7.00 1,095 MAX VALUE 294.04 2.76 0.45 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	322	119.24	105.00	4,531	MAX VALUE	175.03	72.52	0.61	3.39
Variables per cluster	10	82	28.82	23.00	1,095	MAX VALUE	121.78	17.94	0.62	3.03
Separator constraints	0	191	79.05	73.00	3,004	0	None	43.87	0.55	3.27
Separator variables	0	63	24.08	21.00	915	0	None	13.61	0.57	3.15
Clusters per variable	1	10	6.08	7.00	1,095	MAX VALUE	294.04	2.76	0.45	2.19

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 179
Triangles: 100
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Primal1.json

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

Clustering coefficient 0.07 0.33 0.20 0.20 7.89 0.00 -67.29 0.06 0.31 3.02

Degree 5 13 9.00 9.00 360 4.79e+37 86.76 2.09 0.23 2.05

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.50 3.00 626 MAX VALUE 222.06 0.53 0.15 0.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.33	0.20	0.20	7.89	0.00	-67.29	0.06	0.31	3.02
Degree	5	13	9.00	9.00	360	4.79e+37	86.76	2.09	0.23	2.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.50	3.00	626	MAX VALUE	222.06	0.53	0.15	0.77

Triangulated primal graph

Density: 50.51%
MCB compute time (ms): 15
MCB cycles: 358
Triangles: 2,276

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

Clustering coefficient 0.60 1.00 0.83 0.80 33.34 0.00 -7.73 0.13 0.15 2.87

Degree 5 32 19.70 24.50 788 MAX VALUE 112.58 9.51 0.48 2.77

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,074 MAX VALUE 393.30 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	0.83	0.80	33.34	0.00	-7.73	0.13	0.15	2.87
Degree	5	32	19.70	24.50	788	MAX VALUE	112.58	9.51	0.48	2.77
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,074	MAX VALUE	393.30	0.00	0.00	0.00

Dual graph

Density: 9.48%
MCB compute time (ms): 317
MCB cycles: 1,587
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Dual1.json

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

Clustering coefficient 0.44 0.59 0.50 0.50 89.90 0.00 -125.16 0.02 0.05 4.05

Degree 9 23 16.97 17.00 3,054 MAX VALUE 507.38 2.61 0.15 2.34

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,053 MAX VALUE 1,826.86 0.40 0.13 0.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.59	0.50	0.50	89.90	0.00	-125.16	0.02	0.05	4.05
Degree	9	23	16.97	17.00	3,054	MAX VALUE	507.38	2.61	0.15	2.34
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,053	MAX VALUE	1,826.86	0.40	0.13	0.50

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 67
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 224.47 0.73 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.78 7.00 956 MAX VALUE 267.66 1.17 0.17 1.55

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	224.47	0.73	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.78	7.00	956	MAX VALUE	267.66	1.17	0.17	1.55

Triangulated dual graph

Density: 45.10%
Triangles: 184,805

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

Clustering coefficient 0.71 1.00 0.83 0.80 149.31 0.00 -34.73 0.09 0.11 4.47

Degree 9 124 80.73 100.00 14,532 MAX VALUE 754.58 40.12 0.50 3.61

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	0.83	0.80	149.31	0.00	-34.73	0.09	0.11	4.47
Degree	9	124	80.73	100.00	14,532	MAX VALUE	754.58	40.12	0.50	3.61
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.15%

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

Clustering coefficient 0.51 1.00 0.80 0.75 144.73 0.00 -42.41 0.15 0.19 3.32

Degree 2 64 21.74 7.00 3,914 MAX VALUE 424.99 23.89 1.10 3.07

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	0.51	1.00	0.80	0.75	144.73	0.00	-42.41	0.15	0.19	3.32
Degree	2	64	21.74	7.00	3,914	MAX VALUE	424.99	23.89	1.10	3.07
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-96-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 211.53 2.84 0.87 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.68 6.00 942 MAX VALUE 266.45 0.95 0.14 0.64

XCSP 2.1 Benchmarks