XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-25-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:22
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 250

General features

Coarse blocks: 8,000
Value tables: 40

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

Arity 2 2 2.00 2.00 500 MAX VALUE 173.29 0.00 0.00 0.00

Coarse blocks size 4 16 10.39 10.00 83,116 MAX VALUE 18,582.40 1.90 0.18 2.06

Relational linkage 0.25 0.62 0.45 0.44 289.00 0.00 -517.97 0.07 0.16 1.57

Tightness 0.27 0.43 0.35 0.35 87.66 0.00 -262.89 0.03 0.08 3.36

Tuples 145 187 166.23 166.00 41,558 MAX VALUE 1,278.09 7.57 0.05 3.36

Values 16 16 16.00 16.00 640 MAX VALUE 110.90 0.00 0.00 0.00

Value table constraints 7 18 12.50 12.00 500 MAX VALUE 100.14 2.54 0.20 2.23

Value table partitions 16 16 16.00 16.00 640 MAX VALUE 110.90 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	500	MAX VALUE	173.29	0.00	0.00	0.00
Coarse blocks size	4	16	10.39	10.00	83,116	MAX VALUE	18,582.40	1.90	0.18	2.06
Relational linkage	0.25	0.62	0.45	0.44	289.00	0.00	-517.97	0.07	0.16	1.57
Tightness	0.27	0.43	0.35	0.35	87.66	0.00	-262.89	0.03	0.08	3.36
Tuples	145	187	166.23	166.00	41,558	MAX VALUE	1,278.09	7.57	0.05	3.36
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	7	18	12.50	12.00	500	MAX VALUE	100.14	2.54	0.20	2.23
Value table partitions	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 16
Number of leaves: 6
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Tree1.json

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

Cluster constraints 11 106 52.62 45.00 842 2.46e+26 60.77 28.92 0.55 2.69

Variables per cluster 8 25 16.31 15.50 261 1.04e+19 43.79 5.32 0.33 2.22

Separator constraints 0 97 37.00 29.00 592 0 None 27.64 0.75 2.69

Separator variables 0 24 13.81 14.00 221 0 None 6.00 0.43 2.34

Clusters per var 1 13 6.53 7.00 261 3.39e+27 63.39 3.92 0.60 2.44

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	106	52.62	45.00	842	2.46e+26	60.77	28.92	0.55	2.69
Variables per cluster	8	25	16.31	15.50	261	1.04e+19	43.79	5.32	0.33	2.22
Separator constraints	0	97	37.00	29.00	592	0	None	27.64	0.75	2.69
Separator variables	0	24	13.81	14.00	221	0	None	6.00	0.43	2.34
Clusters per var	1	13	6.53	7.00	261	3.39e+27	63.39	3.92	0.60	2.44

Dual tree decomposition

Number of clusters: 38
Number of leaves: 18
Tree depth: 5
CIR: 0.12
Independent Cluster Pairs: 81
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/DualTree1.json

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

Cluster constraints 49 861 268.58 214.00 10,206 MAX VALUE 204.20 190.10 0.71 3.60

Variables per cluster 14 133 43.13 31.00 1,639 MAX VALUE 136.34 28.74 0.67 3.37

Separator constraints 0 451 189.53 168.50 7,202 0 None 111.17 0.59 3.60

Separator variables 0 95 36.55 29.00 1,389 0 None 21.71 0.59 3.37

Clusters per variable 1 10 6.56 8.00 1,639 MAX VALUE 437.75 2.48 0.38 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	49	861	268.58	214.00	10,206	MAX VALUE	204.20	190.10	0.71	3.60
Variables per cluster	14	133	43.13	31.00	1,639	MAX VALUE	136.34	28.74	0.67	3.37
Separator constraints	0	451	189.53	168.50	7,202	0	None	111.17	0.59	3.60
Separator variables	0	95	36.55	29.00	1,389	0	None	21.71	0.59	3.37
Clusters per variable	1	10	6.56	8.00	1,639	MAX VALUE	437.75	2.48	0.38	2.03

Primal graph

Density: 32.05%
MCB compute time (ms): 7
MCB cycles: 228
Triangles: 319
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Primal1.json

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

Clustering coefficient 0.18 0.47 0.32 0.32 12.78 0.00 -46.48 0.06 0.20 3.35

Degree 7 18 12.50 12.00 500 MAX VALUE 100.14 2.54 0.20 2.23

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.07 3.00 699 MAX VALUE 254.80 0.25 0.08 0.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.18	0.47	0.32	0.32	12.78	0.00	-46.48	0.06	0.20	3.35
Degree	7	18	12.50	12.00	500	MAX VALUE	100.14	2.54	0.20	2.23
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.07	3.00	699	MAX VALUE	254.80	0.25	0.08	0.24

Triangulated primal graph

Density: 66.79%
MCB compute time (ms): 23
MCB cycles: 489
Triangles: 4,004

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

Clustering coefficient 0.71 1.00 0.87 0.86 34.61 0.00 -6.00 0.09 0.10 3.42

Degree 7 36 26.05 30.00 1,042 MAX VALUE 127.01 8.94 0.34 2.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,467 MAX VALUE 537.22 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.87	0.86	34.61	0.00	-6.00	0.09	0.10	3.42
Degree	7	36	26.05	30.00	1,042	MAX VALUE	127.01	8.94	0.34	2.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,467	MAX VALUE	537.22	0.00	0.00	0.00

Dual graph

Density: 9.65%
MCB compute time (ms): 928
MCB cycles: 4,101
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Dual1.json

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

Clustering coefficient 0.46 0.57 0.50 0.50 125.94 0.00 -171.55 0.02 0.03 4.48

Degree 13 32 24.03 24.00 6,008 MAX VALUE 792.20 3.38 0.14 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.13 3.00 12,837 MAX VALUE 4,658.90 0.34 0.11 0.39

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.57	0.50	0.50	125.94	0.00	-171.55	0.02	0.03	4.48
Degree	13	32	24.03	24.00	6,008	MAX VALUE	792.20	3.38	0.14	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.13	3.00	12,837	MAX VALUE	4,658.90	0.34	0.11	0.39

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 314
MCB cycles: 211

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

Clustering coefficient 0.00 1.00 0.01 0.00 1.50 0.00 None 0.07 11.20 0.08

Degree 2 6 3.68 4.00 920 MAX VALUE 319.66 0.82 0.22 1.17

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.78 7.00 1,430 MAX VALUE 400.74 1.09 0.16 1.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.01	0.00	1.50	0.00	None	0.07	11.20	0.08
Degree	2	6	3.68	4.00	920	MAX VALUE	319.66	0.82	0.22	1.17
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.78	7.00	1,430	MAX VALUE	400.74	1.09	0.16	1.46

Triangulated dual graph

Density: 53.24%
Triangles: 691,942

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

Clustering coefficient 0.74 1.00 0.85 0.82 211.81 0.00 -42.43 0.08 0.09 4.80

Degree 13 190 132.58 168.00 33,144 MAX VALUE 1,181.33 57.46 0.43 3.76

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	0.74	1.00	0.85	0.82	211.81	0.00	-42.43	0.08	0.09	4.80
Degree	13	190	132.58	168.00	33,144	MAX VALUE	1,181.33	57.46	0.43	3.76
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.00%

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

Clustering coefficient 0.50 1.00 0.82 0.76 204.86 0.00 -53.80 0.15 0.18 3.40

Degree 2 87 27.38 7.00 6,846 MAX VALUE 615.19 32.27 1.18 3.17

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	0.50	1.00	0.82	0.76	204.86	0.00	-53.80	0.15	0.18	3.40
Degree	2	87	27.38	7.00	6,846	MAX VALUE	615.19	32.27	1.18	3.17
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 113
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-25-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 18 3.45 2.00 1,000 MAX VALUE 273.43 3.74 1.09 0.71

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.05 6.00 1,276 MAX VALUE 379.50 0.30 0.05 0.11

XCSP 2.1 Benchmarks