XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-3-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 4 21 12.47 12.00 112,262 MAX VALUE 22,522.80 2.48 0.20 2.33

Relational linkage 0.16 0.60 0.36 0.36 357.60 0.00 -1,044.39 0.06 0.18 1.86

Tightness 0.45 0.55 0.50 0.50 90.19 0.00 -124.51 0.02 0.04 3.67

Tuples 283 345 311.84 312.00 56,131 MAX VALUE 1,033.53 11.42 0.04 3.67

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 2 16 9.00 9.00 360 8.02e+36 84.97 3.03 0.34 2.38

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	4	21	12.47	12.00	112,262	MAX VALUE	22,522.80	2.48	0.20	2.33
Relational linkage	0.16	0.60	0.36	0.36	357.60	0.00	-1,044.39	0.06	0.18	1.86
Tightness	0.45	0.55	0.50	0.50	90.19	0.00	-124.51	0.02	0.04	3.67
Tuples	283	345	311.84	312.00	56,131	MAX VALUE	1,033.53	11.42	0.04	3.67
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	16	9.00	9.00	360	8.02e+36	84.97	3.03	0.34	2.38
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: 20
Number of leaves: 11
Tree depth: 4
CIR: 0.20
Independent Cluster Pairs: 35
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Tree1.json

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

Cluster constraints 2 52 21.75 17.50 435 5.97e+23 54.75 15.72 0.72 2.79

Variables per cluster 3 21 10.95 9.50 219 4.50e+19 45.25 5.34 0.49 2.42

Separator constraints 0 40 12.75 7.50 255 0 None 12.74 1.00 2.69

Separator variables 0 19 8.95 7.00 179 0 None 5.24 0.59 2.42

Clusters per var 1 12 5.47 6.50 219 1.94e+23 53.62 3.66 0.67 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	52	21.75	17.50	435	5.97e+23	54.75	15.72	0.72	2.79
Variables per cluster	3	21	10.95	9.50	219	4.50e+19	45.25	5.34	0.49	2.42
Separator constraints	0	40	12.75	7.50	255	0	None	12.74	1.00	2.69
Separator variables	0	19	8.95	7.00	179	0	None	5.24	0.59	2.42
Clusters per var	1	12	5.47	6.50	219	1.94e+23	53.62	3.66	0.67	2.16

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.23
Independent Cluster Pairs: 154
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/DualTree1.json

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

Cluster constraints 11 430 127.97 104.00 4,863 MAX VALUE 172.08 98.67 0.77 3.53

Variables per cluster 6 88 28.45 22.00 1,081 MAX VALUE 119.76 19.05 0.67 3.25

Separator constraints 0 231 85.24 75.00 3,239 0 None 60.63 0.71 3.51

Separator variables 0 62 23.71 20.00 901 0 None 14.61 0.62 3.14

Clusters per variable 1 12 6.01 7.00 1,081 MAX VALUE 293.36 2.67 0.44 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	430	127.97	104.00	4,863	MAX VALUE	172.08	98.67	0.77	3.53
Variables per cluster	6	88	28.45	22.00	1,081	MAX VALUE	119.76	19.05	0.67	3.25
Separator constraints	0	231	85.24	75.00	3,239	0	None	60.63	0.71	3.51
Separator variables	0	62	23.71	20.00	901	0	None	14.61	0.62	3.14
Clusters per variable	1	12	6.01	7.00	1,081	MAX VALUE	293.36	2.67	0.44	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 149
Triangles: 152
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Primal1.json

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

Clustering coefficient 0.00 0.53 0.26 0.26 10.33 0.00 None 0.11 0.44 3.28

Degree 2 16 9.00 9.00 360 8.02e+36 84.97 3.03 0.34 2.38

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.22 3.00 480 MAX VALUE 173.12 0.43 0.13 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.53	0.26	0.26	10.33	0.00	None	0.11	0.44	3.28
Degree	2	16	9.00	9.00	360	8.02e+36	84.97	3.03	0.34	2.38
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.22	3.00	480	MAX VALUE	173.12	0.43	0.13	0.55

Triangulated primal graph

Density: 49.87%
MCB compute time (ms): 12
MCB cycles: 356
Triangles: 2,316

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

Clustering coefficient 0.64 1.00 0.84 0.80 33.54 0.00 -7.45 0.12 0.14 2.87

Degree 2 31 19.45 25.50 778 MAX VALUE 110.58 9.65 0.50 2.77

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,068 MAX VALUE 391.11 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.84	0.80	33.54	0.00	-7.45	0.12	0.14	2.87
Degree	2	31	19.45	25.50	778	MAX VALUE	110.58	9.65	0.50	2.77
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,068	MAX VALUE	391.11	0.00	0.00	0.00

Dual graph

Density: 10.08%
MCB compute time (ms): 302
MCB cycles: 1,597
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-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 91.70 0.00 -121.83 0.04 0.07 4.27

Degree 5 28 18.04 18.00 3,248 MAX VALUE 514.68 4.25 0.24 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.09 3.00 4,940 MAX VALUE 1,796.90 0.31 0.10 0.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.67	0.51	0.50	91.70	0.00	-121.83	0.04	0.07	4.27
Degree	5	28	18.04	18.00	3,248	MAX VALUE	514.68	4.25	0.24	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.09	3.00	4,940	MAX VALUE	1,796.90	0.31	0.10	0.32

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 66
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 6 3.56 3.00 640 MAX VALUE 224.36 0.76 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.57 7.00 926 MAX VALUE 262.83 1.20 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	6	3.56	3.00	640	MAX VALUE	224.36	0.76	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.57	7.00	926	MAX VALUE	262.83	1.20	0.18	1.58

Triangulated dual graph

Density: 46.21%
Triangles: 197,120

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

Clustering coefficient 0.67 1.00 0.83 0.80 150.11 0.00 -33.60 0.09 0.10 4.64

Degree 5 134 82.71 93.00 14,888 MAX VALUE 756.78 41.00 0.50 3.99

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	0.67	1.00	0.83	0.80	150.11	0.00	-33.60	0.09	0.10	4.64
Degree	5	134	82.71	93.00	14,888	MAX VALUE	756.78	41.00	0.50	3.99
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.46%

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

Clustering coefficient 0.51 1.00 0.80 0.72 143.40 0.00 -44.37 0.16 0.20 3.26

Degree 2 64 20.52 7.00 3,694 MAX VALUE 420.29 22.55 1.10 3.01

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	0.72	143.40	0.00	-44.37	0.16	0.20	3.26
Degree	2	64	20.52	7.00	3,694	MAX VALUE	420.29	22.55	1.10	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 38
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-3-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 16 3.27 2.00 720 MAX VALUE 209.74 2.99 0.91 0.88

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.37 6.00 898 MAX VALUE 260.05 0.81 0.13 0.50

XCSP 2.1 Benchmarks