XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-98-ext
Number of variables: 40
Number of constraints: 414
Satisfiable: True
Timestamp: 2025-07-27 21:30:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 40
Number of constraints: 414

General features

Coarse blocks: 9,108
Value tables: 40

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

Arity 2 2 2.00 2.00 828 MAX VALUE 286.96 0.00 0.00 0.00

Coarse blocks size 3 11 8.78 9.00 79,988 MAX VALUE 19,674.50 1.33 0.15 1.68

Relational linkage 0.27 0.73 0.55 0.55 243.64 0.00 -265.52 0.08 0.15 1.29

Tightness 0.09 0.33 0.20 0.20 83.47 0.00 -670.21 0.04 0.18 2.88

Tuples 81 110 96.60 97.00 39,994 MAX VALUE 1,891.79 4.46 0.05 2.88

Values 11 11 11.00 11.00 440 MAX VALUE 95.92 0.00 0.00 0.00

Value table constraints 10 28 20.70 20.50 828 MAX VALUE 120.50 3.69 0.18 2.55

Value table partitions 11 11 11.00 11.00 440 MAX VALUE 95.92 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	828	MAX VALUE	286.96	0.00	0.00	0.00
Coarse blocks size	3	11	8.78	9.00	79,988	MAX VALUE	19,674.50	1.33	0.15	1.68
Relational linkage	0.27	0.73	0.55	0.55	243.64	0.00	-265.52	0.08	0.15	1.29
Tightness	0.09	0.33	0.20	0.20	83.47	0.00	-670.21	0.04	0.18	2.88
Tuples	81	110	96.60	97.00	39,994	MAX VALUE	1,891.79	4.46	0.05	2.88
Values	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00
Value table constraints	10	28	20.70	20.50	828	MAX VALUE	120.50	3.69	0.18	2.55
Value table partitions	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00

Tree decomposition

Number of clusters: 11
Number of leaves: 6
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Tree1.json

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

Cluster constraints 35 254 146.73 94.00 1,614 9.06e+22 52.86 81.74 0.56 2.40

Variables per cluster 11 30 21.73 18.00 239 2.94e+14 33.32 6.63 0.31 1.80

Separator constraints 0 237 109.09 73.00 1,200 0 None 80.71 0.74 2.40

Separator variables 0 29 18.09 16.00 199 0 None 8.36 0.46 1.97

Clusters per var 1 10 5.97 7.00 239 4.46e+27 63.66 2.69 0.45 1.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	35	254	146.73	94.00	1,614	9.06e+22	52.86	81.74	0.56	2.40
Variables per cluster	11	30	21.73	18.00	239	2.94e+14	33.32	6.63	0.31	1.80
Separator constraints	0	237	109.09	73.00	1,200	0	None	80.71	0.74	2.40
Separator variables	0	29	18.09	16.00	199	0	None	8.36	0.46	1.97
Clusters per var	1	10	5.97	7.00	239	4.46e+27	63.66	2.69	0.45	1.93

Dual tree decomposition

Number of clusters: 38
Number of leaves: 19
Tree depth: 5
CIR: 0.02
Independent Cluster Pairs: 15
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/DualTree1.json

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

Cluster constraints 201 3,177 849.63 566.50 32,286 MAX VALUE 246.69 693.44 0.82 3.64

Variables per cluster 27 254 76.82 51.00 2,919 MAX VALUE 157.50 55.37 0.72 3.42

Separator constraints 0 1,783 627.84 508.00 23,858 0 None 403.96 0.64 3.64

Separator variables 0 190 65.92 48.50 2,505 0 None 42.10 0.64 3.49

Clusters per variable 1 10 7.05 8.00 2,919 MAX VALUE 770.50 2.21 0.31 1.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	201	3,177	849.63	566.50	32,286	MAX VALUE	246.69	693.44	0.82	3.64
Variables per cluster	27	254	76.82	51.00	2,919	MAX VALUE	157.50	55.37	0.72	3.42
Separator constraints	0	1,783	627.84	508.00	23,858	0	None	403.96	0.64	3.64
Separator variables	0	190	65.92	48.50	2,505	0	None	42.10	0.64	3.49
Clusters per variable	1	10	7.05	8.00	2,919	MAX VALUE	770.50	2.21	0.31	1.84

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,511
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Primal1.json

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

Clustering coefficient 0.47 0.61 0.54 0.54 21.59 0.00 -24.73 0.03 0.06 3.52

Degree 10 28 20.70 20.50 828 MAX VALUE 120.50 3.69 0.18 2.55

Eccentricity 2 2 2.00 2.00 80 1.10e+12 27.73 0.00 0.00 0.00

MCB cycle size 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	0.61	0.54	0.54	21.59	0.00	-24.73	0.03	0.06	3.52
Degree	10	28	20.70	20.50	828	MAX VALUE	120.50	3.69	0.18	2.55
Eccentricity	2	2	2.00	2.00	80	1.10e+12	27.73	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 81.28%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,145

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

Clustering coefficient 0.83 1.00 0.91 0.90 36.49 0.02 -3.73 0.05 0.05 3.00

Degree 10 38 31.70 35.00 1,268 MAX VALUE 136.60 7.43 0.23 2.15

Eccentricity 2 2 2.00 2.00 80 1.10e+12 27.73 0.00 0.00 0.00

MCB cycle size 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	0.83	1.00	0.91	0.90	36.49	0.02	-3.73	0.05	0.05	3.00
Degree	10	38	31.70	35.00	1,268	MAX VALUE	136.60	7.43	0.23	2.15
Eccentricity	2	2	2.00	2.00	80	1.10e+12	27.73	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.86%
MCB compute time (ms): 8,513
MCB cycles: 10,214
Triangles: 57,600
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Dual1.json

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

Clustering coefficient 0.49 0.62 0.51 0.51 210.99 0.00 -279.20 0.01 0.03 5.18

Degree 26 53 40.72 41.00 16,856 MAX VALUE 1,531.57 4.80 0.12 2.97

Eccentricity 3 3 3.00 3.00 1,242 MAX VALUE 454.82 0.00 0.00 0.00

MCB cycle size 3 4 3.04 3.00 31,029 MAX VALUE 11,332.60 0.19 0.06 0.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.62	0.51	0.51	210.99	0.00	-279.20	0.01	0.03	5.18
Degree	26	53	40.72	41.00	16,856	MAX VALUE	1,531.57	4.80	0.12	2.97
Eccentricity	3	3	3.00	3.00	1,242	MAX VALUE	454.82	0.00	0.00	0.00
MCB cycle size	3	4	3.04	3.00	31,029	MAX VALUE	11,332.60	0.19	0.06	0.16

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,931
MCB cycles: 375

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.02 12.17 0.05

Degree 2 7 3.81 4.00 1,576 MAX VALUE 542.30 0.91 0.24 1.23

Eccentricity 6 10 8.08 8.00 3,347 MAX VALUE 863.70 0.70 0.09 1.05

MCB cycle size 3 9 6.59 7.00 2,472 MAX VALUE 700.13 1.22 0.18 1.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.02	12.17	0.05
Degree	2	7	3.81	4.00	1,576	MAX VALUE	542.30	0.91	0.24	1.23
Eccentricity	6	10	8.08	8.00	3,347	MAX VALUE	863.70	0.70	0.09	1.05
MCB cycle size	3	9	6.59	7.00	2,472	MAX VALUE	700.13	1.22	0.18	1.59

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.34%

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

Clustering coefficient 0.49 1.00 0.84 0.80 346.19 0.00 -79.76 0.14 0.16 3.77

Degree 2 137 42.72 8.00 17,686 MAX VALUE 1,113.24 53.91 1.26 3.29

Eccentricity 3 5 3.77 4.00 1,562 MAX VALUE 545.46 0.53 0.14 0.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	0.84	0.80	346.19	0.00	-79.76	0.14	0.16	3.77
Degree	2	137	42.72	8.00	17,686	MAX VALUE	1,113.24	53.91	1.26	3.29
Eccentricity	3	5	3.77	4.00	1,562	MAX VALUE	545.46	0.53	0.14	0.78

Incidence graph

Density: 0.81%
MCB compute time (ms): 631
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-98-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 28 3.65 2.00 1,656 MAX VALUE 407.46 5.41 1.48 0.52

Eccentricity 5 6 5.91 6.00 2,684 MAX VALUE 806.17 0.28 0.05 0.30

MCB cycle size 6 6 6.00 6.00 2,250 MAX VALUE 671.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks