XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-2-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:32
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 135

General features

Coarse blocks: 10,800
Value tables: 40

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

Arity 2 2 2.00 2.00 270 MAX VALUE 93.57 0.00 0.00 0.00

Coarse blocks size 3 26 13.94 14.00 150,576 MAX VALUE 28,186.30 3.02 0.22 2.52

Relational linkage 0.07 0.40 0.25 0.25 403.45 0.00 -2,235.79 0.05 0.19 2.06

Tightness 0.62 0.69 0.65 0.65 87.94 0.00 -57.88 0.01 0.02 3.94

Tuples 503 606 557.69 560.00 75,288 MAX VALUE 853.62 21.06 0.04 3.94

Values 40 40 40.00 40.00 1,600 MAX VALUE 147.56 0.00 0.00 0.00

Value table constraints 3 13 6.75 6.50 270 1.49e+32 74.08 2.30 0.34 2.13

Value table partitions 40 40 40.00 40.00 1,600 MAX VALUE 147.56 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	270	MAX VALUE	93.57	0.00	0.00	0.00
Coarse blocks size	3	26	13.94	14.00	150,576	MAX VALUE	28,186.30	3.02	0.22	2.52
Relational linkage	0.07	0.40	0.25	0.25	403.45	0.00	-2,235.79	0.05	0.19	2.06
Tightness	0.62	0.69	0.65	0.65	87.94	0.00	-57.88	0.01	0.02	3.94
Tuples	503	606	557.69	560.00	75,288	MAX VALUE	853.62	21.06	0.04	3.94
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	3	13	6.75	6.50	270	1.49e+32	74.08	2.30	0.34	2.13
Value table partitions	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00

Tree decomposition

Number of clusters: 24
Number of leaves: 12
Tree depth: 4
CIR: 0.19
Independent Cluster Pairs: 48
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Tree1.json

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

Cluster constraints 3 30 11.83 8.50 284 3.77e+23 54.29 7.94 0.67 2.53

Variables per cluster 4 17 8.58 7.00 206 2.51e+21 49.27 3.89 0.45 2.16

Separator constraints 0 25 6.21 3.50 149 0 None 6.87 1.11 2.41

Separator variables 0 15 6.92 6.00 166 0 None 3.76 0.54 2.16

Clusters per var 1 13 5.15 4.00 206 3.41e+21 49.58 3.98 0.77 2.13

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	30	11.83	8.50	284	3.77e+23	54.29	7.94	0.67	2.53
Variables per cluster	4	17	8.58	7.00	206	2.51e+21	49.27	3.89	0.45	2.16
Separator constraints	0	25	6.21	3.50	149	0	None	6.87	1.11	2.41
Separator variables	0	15	6.92	6.00	166	0	None	3.76	0.54	2.16
Clusters per var	1	13	5.15	4.00	206	3.41e+21	49.58	3.98	0.77	2.13

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 6
CIR: 0.34
Independent Cluster Pairs: 224
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/DualTree1.json

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

Cluster constraints 13 165 59.74 49.50 2,270 MAX VALUE 146.57 40.59 0.68 3.42

Variables per cluster 7 55 19.71 16.00 749 MAX VALUE 107.37 11.90 0.60 3.12

Separator constraints 0 95 36.53 31.00 1,388 0 None 24.36 0.67 3.39

Separator variables 0 40 16.16 14.50 614 0 None 9.10 0.56 2.95

Clusters per variable 1 11 5.55 6.00 749 MAX VALUE 204.64 2.86 0.52 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	165	59.74	49.50	2,270	MAX VALUE	146.57	40.59	0.68	3.42
Variables per cluster	7	55	19.71	16.00	749	MAX VALUE	107.37	11.90	0.60	3.12
Separator constraints	0	95	36.53	31.00	1,388	0	None	24.36	0.67	3.39
Separator variables	0	40	16.16	14.50	614	0	None	9.10	0.56	2.95
Clusters per variable	1	11	5.55	6.00	749	MAX VALUE	204.64	2.86	0.52	2.28

Primal graph

Density: 17.31%
MCB compute time (ms): 2
MCB cycles: 118
Triangles: 59
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.20 0.20 8.04 0.00 None 0.11 0.53 3.00

Degree 3 13 6.75 6.50 270 1.49e+32 74.08 2.30 0.34 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.58 4.00 422 MAX VALUE 148.75 0.60 0.17 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.20	0.20	8.04	0.00	None	0.11	0.53	3.00
Degree	3	13	6.75	6.50	270	1.49e+32	74.08	2.30	0.34	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.58	4.00	422	MAX VALUE	148.75	0.60	0.17	0.88

Triangulated primal graph

Density: 38.72%
MCB compute time (ms): 7
MCB cycles: 267
Triangles: 1,341

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

Clustering coefficient 0.56 1.00 0.81 0.80 32.46 0.00 -9.03 0.15 0.18 2.83

Degree 3 28 15.10 15.00 604 MAX VALUE 99.09 8.85 0.59 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 801 MAX VALUE 293.33 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.56	1.00	0.81	0.80	32.46	0.00	-9.03	0.15	0.18	2.83
Degree	3	28	15.10	15.00	604	MAX VALUE	99.09	8.85	0.59	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	801	MAX VALUE	293.33	0.00	0.00	0.00

Dual graph

Density: 9.75%
MCB compute time (ms): 59
MCB cycles: 1,129
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Dual1.json

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

Clustering coefficient 0.43 0.67 0.51 0.50 68.60 0.00 -91.86 0.04 0.09 3.89

Degree 6 21 13.07 13.00 1,764 MAX VALUE 342.15 3.41 0.26 2.60

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.46 3.00 3,902 MAX VALUE 1,379.33 0.71 0.20 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.67	0.51	0.50	68.60	0.00	-91.86	0.04	0.09	3.89
Degree	6	21	13.07	13.00	1,764	MAX VALUE	342.15	3.41	0.26	2.60
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.46	3.00	3,902	MAX VALUE	1,379.33	0.71	0.20	0.85

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 29
MCB cycles: 96

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 3.41 3.00 460 MAX VALUE 162.56 0.70 0.21 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.67 7.00 640 MAX VALUE 180.39 1.22 0.18 1.58

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	3.41	3.00	460	MAX VALUE	162.56	0.70	0.21	1.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.67	7.00	640	MAX VALUE	180.39	1.22	0.18	1.58

Triangulated dual graph

Density: 38.36%
Triangles: 55,754

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

Clustering coefficient 0.63 1.00 0.81 0.79 109.87 0.00 -28.95 0.11 0.13 4.43

Degree 6 91 51.41 56.00 6,940 MAX VALUE 500.90 28.07 0.55 3.86

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	0.63	1.00	0.81	0.79	109.87	0.00	-28.95	0.11	0.13	4.43
Degree	6	91	51.41	56.00	6,940	MAX VALUE	500.90	28.07	0.55	3.86
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.02%

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

Clustering coefficient 0.49 1.00 0.78 0.71 104.98 0.00 -37.32 0.17 0.22 3.15

Degree 2 51 16.10 7.00 2,174 MAX VALUE 297.00 16.38 1.02 3.05

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	0.49	1.00	0.78	0.71	104.98	0.00	-37.32	0.17	0.22	3.15
Degree	2	51	16.10	7.00	2,174	MAX VALUE	297.00	16.38	1.02	3.05
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 26
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-2-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 3.09 2.00 540 MAX VALUE 167.66 2.28 0.74 1.02

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.81 6.00 654 MAX VALUE 183.23 0.98 0.14 0.68

XCSP 2.1 Benchmarks