XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-12-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 103

General features

Coarse blocks: 16,480
Value tables: 40

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

Arity 2 2 2.00 2.00 206 1.01e+31 71.39 0.00 0.00 0.00

Coarse blocks size 3 31 16.00 16.00 263,622 MAX VALUE 45,254.40 3.58 0.22 2.69

Relational linkage 0.04 0.26 0.15 0.15 481.34 0.00 -6,126.65 0.03 0.19 2.27

Tightness 0.79 0.81 0.80 0.80 82.40 0.00 -22.98 0.01 0.01 4.19

Tuples 1,204 1,355 1,279.72 1,278.00 131,811 MAX VALUE 736.87 34.57 0.03 4.19

Values 80 80 80.00 80.00 3,200 MAX VALUE 175.28 0.00 0.00 0.00

Value table constraints 2 9 5.15 5.00 206 2.36e+27 63.03 1.75 0.34 1.88

Value table partitions 80 80 80.00 80.00 3,200 MAX VALUE 175.28 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	206	1.01e+31	71.39	0.00	0.00	0.00
Coarse blocks size	3	31	16.00	16.00	263,622	MAX VALUE	45,254.40	3.58	0.22	2.69
Relational linkage	0.04	0.26	0.15	0.15	481.34	0.00	-6,126.65	0.03	0.19	2.27
Tightness	0.79	0.81	0.80	0.80	82.40	0.00	-22.98	0.01	0.01	4.19
Tuples	1,204	1,355	1,279.72	1,278.00	131,811	MAX VALUE	736.87	34.57	0.03	4.19
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	9	5.15	5.00	206	2.36e+27	63.03	1.75	0.34	1.88
Value table partitions	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00

Tree decomposition

Number of clusters: 28
Number of leaves: 14
Tree depth: 5
CIR: 0.30
Independent Cluster Pairs: 106
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Tree1.json

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

Cluster constraints 2 12 6.32 6.00 177 8.75e+20 48.22 2.93 0.46 2.12

Variables per cluster 3 13 6.68 6.00 187 1.04e+22 50.70 2.84 0.43 2.23

Separator constraints 0 8 2.64 2.00 74 0 None 2.50 0.94 1.93

Separator variables 0 11 5.25 4.50 147 0 None 2.76 0.53 2.23

Clusters per var 1 16 4.67 3.00 187 1.02e+19 43.76 4.17 0.89 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	12	6.32	6.00	177	8.75e+20	48.22	2.93	0.46	2.12
Variables per cluster	3	13	6.68	6.00	187	1.04e+22	50.70	2.84	0.43	2.23
Separator constraints	0	8	2.64	2.00	74	0	None	2.50	0.94	1.93
Separator variables	0	11	5.25	4.50	147	0	None	2.76	0.53	2.23
Clusters per var	1	16	4.67	3.00	187	1.02e+19	43.76	4.17	0.89	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 12
Tree depth: 6
CIR: 0.42
Independent Cluster Pairs: 280
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/DualTree1.json

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

Cluster constraints 9 68 29.08 26.50 1,105 MAX VALUE 122.01 15.88 0.55 3.19

Variables per cluster 6 36 13.66 11.50 519 MAX VALUE 94.42 7.59 0.56 2.77

Separator constraints 0 40 16.21 12.50 616 0 None 10.21 0.63 3.14

Separator variables 0 27 10.95 10.00 416 0 None 5.87 0.54 2.72

Clusters per variable 1 10 5.04 5.00 519 MAX VALUE 144.09 2.85 0.57 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	68	29.08	26.50	1,105	MAX VALUE	122.01	15.88	0.55	3.19
Variables per cluster	6	36	13.66	11.50	519	MAX VALUE	94.42	7.59	0.56	2.77
Separator constraints	0	40	16.21	12.50	616	0	None	10.21	0.63	3.14
Separator variables	0	27	10.95	10.00	416	0	None	5.87	0.54	2.72
Clusters per variable	1	10	5.04	5.00	519	MAX VALUE	144.09	2.85	0.57	2.25

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 71
Triangles: 27
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Primal1.json

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

Clustering coefficient 0.00 0.67 0.17 0.15 6.63 0.00 None 0.14 0.85 2.47

Degree 2 9 5.15 5.00 206 2.36e+27 63.03 1.75 0.34 1.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.80 4.00 270 MAX VALUE 93.62 0.70 0.19 1.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	0.17	0.15	6.63	0.00	None	0.14	0.85	2.47
Degree	2	9	5.15	5.00	206	2.36e+27	63.03	1.75	0.34	1.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.80	4.00	270	MAX VALUE	93.62	0.70	0.19	1.02

Triangulated primal graph

Density: 28.85%
MCB compute time (ms): 2
MCB cycles: 195
Triangles: 705

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

Clustering coefficient 0.45 1.00 0.79 0.74 31.49 0.00 -10.75 0.19 0.24 2.67

Degree 2 27 11.25 9.00 450 1.17e+37 85.35 7.67 0.68 2.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 585 MAX VALUE 214.23 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.79	0.74	31.49	0.00	-10.75	0.19	0.24	2.67
Degree	2	27	11.25	9.00	450	1.17e+37	85.35	7.67	0.68	2.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	585	MAX VALUE	214.23	0.00	0.00	0.00

Dual graph

Density: 9.31%
MCB compute time (ms): 39
MCB cycles: 397
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Dual1.json

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

Clustering coefficient 0.40 0.75 0.50 0.50 51.79 0.00 -71.46 0.06 0.12 3.25

Degree 5 15 9.50 10.00 978 MAX VALUE 228.56 2.31 0.24 2.20

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.15 3.00 1,249 MAX VALUE 452.15 0.42 0.13 0.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	0.75	0.50	0.50	51.79	0.00	-71.46	0.06	0.12	3.25
Degree	5	15	9.50	10.00	978	MAX VALUE	228.56	2.31	0.24	2.20
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.15	3.00	1,249	MAX VALUE	452.15	0.42	0.13	0.43

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 12
MCB cycles: 64

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 4 3.22 3.00 332 MAX VALUE 118.95 0.56 0.17 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.89 7.00 441 MAX VALUE 121.97 1.44 0.21 1.70

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	4	3.22	3.00	332	MAX VALUE	118.95	0.56	0.17	0.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.89	7.00	441	MAX VALUE	121.97	1.44	0.21	1.70

Triangulated dual graph

Density: 31.49%
Triangles: 16,518

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

Clustering coefficient 0.60 1.00 0.79 0.79 81.77 0.00 -24.91 0.12 0.15 4.14

Degree 5 61 32.12 29.00 3,308 MAX VALUE 331.12 19.45 0.61 3.51

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	0.60	1.00	0.79	0.79	81.77	0.00	-24.91	0.12	0.15	4.14
Degree	5	61	32.12	29.00	3,308	MAX VALUE	331.12	19.45	0.61	3.51
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.16%

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

Clustering coefficient 0.44 1.00 0.76 0.67 78.42 0.00 -31.45 0.19 0.25 2.87

Degree 2 39 12.41 7.00 1,278 MAX VALUE 210.58 11.86 0.96 2.80

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	0.44	1.00	0.76	0.67	78.42	0.00	-31.45	0.19	0.25	2.87
Degree	2	39	12.41	7.00	1,278	MAX VALUE	210.58	11.86	0.96	2.80
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 12
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-12-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 9 2.88 2.00 412 MAX VALUE 134.42 1.69 0.59 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.41 8.00 474 MAX VALUE 127.17 1.31 0.18 0.96

XCSP 2.1 Benchmarks