XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-66-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
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 3 21 12.46 12.00 112,166 MAX VALUE 22,507.50 2.52 0.20 2.34

Relational linkage 0.12 0.56 0.35 0.36 352.48 0.00 -1,060.94 0.06 0.18 1.88

Tightness 0.45 0.56 0.50 0.50 90.27 0.00 -124.39 0.02 0.04 3.79

Tuples 277 346 311.57 312.00 56,083 MAX VALUE 1,033.34 12.94 0.04 3.79

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

Value table constraints 3 15 9.00 9.00 360 3.05e+37 86.31 2.37 0.26 2.19

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	3	21	12.46	12.00	112,166	MAX VALUE	22,507.50	2.52	0.20	2.34
Relational linkage	0.12	0.56	0.35	0.36	352.48	0.00	-1,060.94	0.06	0.18	1.88
Tightness	0.45	0.56	0.50	0.50	90.27	0.00	-124.39	0.02	0.04	3.79
Tuples	277	346	311.57	312.00	56,083	MAX VALUE	1,033.34	12.94	0.04	3.79
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	15	9.00	9.00	360	3.05e+37	86.31	2.37	0.26	2.19
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: 21
Number of leaves: 9
Tree depth: 5
CIR: 0.06
Independent Cluster Pairs: 11
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Tree1.json

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

Cluster constraints 3 53 22.62 16.00 475 1.73e+26 60.42 14.55 0.64 2.91

Variables per cluster 4 20 11.67 10.00 245 3.38e+21 49.57 4.96 0.43 2.52

Separator constraints 0 44 14.05 8.00 295 0 None 13.21 0.94 2.78

Separator variables 0 19 9.76 8.00 205 0 None 5.09 0.52 2.58

Clusters per var 1 14 6.12 6.00 245 4.34e+24 56.73 4.38 0.72 2.33

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	53	22.62	16.00	475	1.73e+26	60.42	14.55	0.64	2.91
Variables per cluster	4	20	11.67	10.00	245	3.38e+21	49.57	4.96	0.43	2.52
Separator constraints	0	44	14.05	8.00	295	0	None	13.21	0.94	2.78
Separator variables	0	19	9.76	8.00	205	0	None	5.09	0.52	2.58
Clusters per var	1	14	6.12	6.00	245	4.34e+24	56.73	4.38	0.72	2.33

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 127
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/DualTree1.json

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

Cluster constraints 38 366 121.03 100.00 4,599 MAX VALUE 175.59 77.10 0.64 3.46

Variables per cluster 12 86 28.68 22.00 1,090 MAX VALUE 121.59 18.02 0.63 3.19

Separator constraints 0 192 80.18 68.50 3,047 0 None 45.63 0.57 3.46

Separator variables 0 59 23.95 19.50 910 0 None 13.68 0.57 3.08

Clusters per variable 1 10 6.06 7.00 1,090 MAX VALUE 293.70 2.72 0.45 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	38	366	121.03	100.00	4,599	MAX VALUE	175.59	77.10	0.64	3.46
Variables per cluster	12	86	28.68	22.00	1,090	MAX VALUE	121.59	18.02	0.63	3.19
Separator constraints	0	192	80.18	68.50	3,047	0	None	45.63	0.57	3.46
Separator variables	0	59	23.95	19.50	910	0	None	13.68	0.57	3.08
Clusters per variable	1	10	6.06	7.00	1,090	MAX VALUE	293.70	2.72	0.45	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 154
Triangles: 117
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Primal1.json

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

Clustering coefficient 0.00 0.40 0.22 0.22 8.71 0.00 None 0.08 0.37 3.28

Degree 3 15 9.00 9.00 360 3.05e+37 86.31 2.37 0.26 2.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.34 3.00 514 MAX VALUE 184.15 0.47 0.14 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.40	0.22	0.22	8.71	0.00	None	0.08	0.37	3.28
Degree	3	15	9.00	9.00	360	3.05e+37	86.31	2.37	0.26	2.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.34	3.00	514	MAX VALUE	184.15	0.47	0.14	0.64

Triangulated primal graph

Density: 50.64%
MCB compute time (ms): 9
MCB cycles: 385
Triangles: 2,310

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

Clustering coefficient 0.63 1.00 0.84 0.82 33.50 0.00 -7.53 0.12 0.15 3.08

Degree 3 32 19.75 23.50 790 MAX VALUE 112.31 9.53 0.48 2.94

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,155 MAX VALUE 422.97 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.84	0.82	33.50	0.00	-7.53	0.12	0.15	3.08
Degree	3	32	19.75	23.50	790	MAX VALUE	112.31	9.53	0.48	2.94
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,155	MAX VALUE	422.97	0.00	0.00	0.00

Dual graph

Density: 9.63%
MCB compute time (ms): 247
MCB cycles: 1,667
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Dual1.json

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

Clustering coefficient 0.46 0.74 0.50 0.50 90.83 0.00 -123.50 0.04 0.07 4.20

Degree 11 26 17.24 17.00 3,104 MAX VALUE 509.75 3.04 0.18 2.49

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,308 MAX VALUE 1,918.29 0.42 0.13 0.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.74	0.50	0.50	90.83	0.00	-123.50	0.04	0.07	4.20
Degree	11	26	17.24	17.00	3,104	MAX VALUE	509.75	3.04	0.18	2.49
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,308	MAX VALUE	1,918.29	0.42	0.13	0.50

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 67
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.73 0.00 None 0.02 5.57 0.17

Degree 2 5 3.56 3.00 640 MAX VALUE 224.47 0.73 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.82 7.00 962 MAX VALUE 267.97 1.25 0.18 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.73	0.00	None	0.02	5.57	0.17
Degree	2	5	3.56	3.00	640	MAX VALUE	224.47	0.73	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.82	7.00	962	MAX VALUE	267.97	1.25	0.18	1.58

Triangulated dual graph

Density: 45.08%
Triangles: 186,204

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

Clustering coefficient 0.71 1.00 0.83 0.80 149.49 0.00 -34.43 0.09 0.11 4.69

Degree 11 127 80.69 85.00 14,524 MAX VALUE 753.67 40.44 0.50 3.91

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	0.71	1.00	0.83	0.80	149.49	0.00	-34.43	0.09	0.11	4.69
Degree	11	127	80.69	85.00	14,524	MAX VALUE	753.67	40.44	0.50	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.48%

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

Clustering coefficient 0.49 1.00 0.79 0.73 142.27 0.00 -46.05 0.16 0.20 3.37

Degree 2 67 20.56 7.50 3,700 MAX VALUE 422.23 22.22 1.08 3.13

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	0.79	0.73	142.27	0.00	-46.05	0.16	0.20	3.37
Degree	2	67	20.56	7.50	3,700	MAX VALUE	422.23	22.22	1.08	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 45
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-66-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 15 3.27 2.00 720 MAX VALUE 211.08 2.88 0.88 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.55 6.00 924 MAX VALUE 263.86 0.89 0.14 0.59

XCSP 2.1 Benchmarks