XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-12-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:23
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 22 12.48 12.00 112,330 MAX VALUE 22,524.00 2.50 0.20 2.33

Relational linkage 0.12 0.56 0.35 0.36 353.68 0.00 -1,057.38 0.06 0.18 1.88

Tightness 0.45 0.54 0.50 0.50 90.14 0.00 -124.61 0.02 0.04 3.61

Tuples 288 346 312.03 312.00 56,165 MAX VALUE 1,033.64 11.02 0.04 3.61

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

Value table constraints 3 13 9.00 9.00 360 1.98e+37 85.88 2.59 0.29 2.22

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	22	12.48	12.00	112,330	MAX VALUE	22,524.00	2.50	0.20	2.33
Relational linkage	0.12	0.56	0.35	0.36	353.68	0.00	-1,057.38	0.06	0.18	1.88
Tightness	0.45	0.54	0.50	0.50	90.14	0.00	-124.61	0.02	0.04	3.61
Tuples	288	346	312.03	312.00	56,165	MAX VALUE	1,033.64	11.02	0.04	3.61
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	13	9.00	9.00	360	1.98e+37	85.88	2.59	0.29	2.22
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: 10
Tree depth: 4
CIR: 0.13
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Tree1.json

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

Cluster constraints 3 61 21.45 16.50 429 2.38e+24 56.13 15.37 0.72 2.93

Variables per cluster 4 21 10.80 9.00 216 6.48e+19 45.62 4.78 0.44 2.29

Separator constraints 0 48 12.45 8.00 249 0 None 12.69 1.02 2.69

Separator variables 0 19 8.80 7.50 176 0 None 4.63 0.53 2.29

Clusters per var 1 12 5.40 6.00 216 2.53e+23 53.89 3.56 0.66 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	61	21.45	16.50	429	2.38e+24	56.13	15.37	0.72	2.93
Variables per cluster	4	21	10.80	9.00	216	6.48e+19	45.62	4.78	0.44	2.29
Separator constraints	0	48	12.45	8.00	249	0	None	12.69	1.02	2.69
Separator variables	0	19	8.80	7.50	176	0	None	4.63	0.53	2.29
Clusters per var	1	12	5.40	6.00	216	2.53e+23	53.89	3.56	0.66	2.14

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.23
Independent Cluster Pairs: 152
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/DualTree1.json

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

Cluster constraints 16 344 125.97 105.00 4,787 MAX VALUE 175.35 84.13 0.67 3.48

Variables per cluster 8 82 28.71 23.00 1,091 MAX VALUE 121.18 18.20 0.63 3.11

Separator constraints 0 213 84.55 78.50 3,213 0 None 51.73 0.61 3.51

Separator variables 0 62 23.97 20.50 911 0 None 13.87 0.58 3.17

Clusters per variable 1 11 6.06 7.00 1,091 MAX VALUE 295.42 2.64 0.44 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	344	125.97	105.00	4,787	MAX VALUE	175.35	84.13	0.67	3.48
Variables per cluster	8	82	28.71	23.00	1,091	MAX VALUE	121.18	18.20	0.63	3.11
Separator constraints	0	213	84.55	78.50	3,213	0	None	51.73	0.61	3.51
Separator variables	0	62	23.97	20.50	911	0	None	13.87	0.58	3.17
Clusters per variable	1	11	6.06	7.00	1,091	MAX VALUE	295.42	2.64	0.44	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 155
Triangles: 128
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.25 0.25 9.83 0.00 None 0.09 0.36 3.33

Degree 3 13 9.00 9.00 360 1.98e+37 85.88 2.59 0.29 2.22

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.29 3.00 510 MAX VALUE 183.23 0.45 0.14 0.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.25	0.25	9.83	0.00	None	0.09	0.36	3.33
Degree	3	13	9.00	9.00	360	1.98e+37	85.88	2.59	0.29	2.22
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.29	3.00	510	MAX VALUE	183.23	0.45	0.14	0.60

Triangulated primal graph

Density: 49.49%
MCB compute time (ms): 8
MCB cycles: 353
Triangles: 2,231

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

Clustering coefficient 0.63 1.00 0.83 0.81 33.39 0.00 -7.62 0.12 0.14 2.96

Degree 3 31 19.30 25.00 772 MAX VALUE 111.02 9.46 0.49 2.65

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,059 MAX VALUE 387.81 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	0.83	0.81	33.39	0.00	-7.62	0.12	0.14	2.96
Degree	3	31	19.30	25.00	772	MAX VALUE	111.02	9.46	0.49	2.65
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,059	MAX VALUE	387.81	0.00	0.00	0.00

Dual graph

Density: 9.77%
MCB compute time (ms): 285
MCB cycles: 1,761
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Dual1.json

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

Clustering coefficient 0.43 0.74 0.51 0.50 91.44 0.00 -122.45 0.04 0.08 4.07

Degree 7 24 17.49 18.00 3,148 MAX VALUE 511.66 3.25 0.19 2.54

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.23 3.00 5,689 MAX VALUE 2,049.84 0.45 0.14 0.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.74	0.51	0.50	91.44	0.00	-122.45	0.04	0.08	4.07
Degree	7	24	17.49	18.00	3,148	MAX VALUE	511.66	3.25	0.19	2.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.23	3.00	5,689	MAX VALUE	2,049.84	0.45	0.14	0.57

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 81
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 0.50 0.00 None 0.02 7.68 0.08

Degree 2 5 3.56 3.00 640 MAX VALUE 224.59 0.72 0.20 1.07

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.85 7.00 966 MAX VALUE 269.14 1.14 0.17 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.50	0.00	None	0.02	7.68	0.08
Degree	2	5	3.56	3.00	640	MAX VALUE	224.59	0.72	0.20	1.07
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.85	7.00	966	MAX VALUE	269.14	1.14	0.17	1.52

Triangulated dual graph

Density: 45.24%
Triangles: 184,702

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

Clustering coefficient 0.70 1.00 0.83 0.81 148.96 0.00 -35.14 0.09 0.11 4.62

Degree 7 128 80.98 94.00 14,576 MAX VALUE 755.62 39.70 0.49 3.90

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	0.70	1.00	0.83	0.81	148.96	0.00	-35.14	0.09	0.11	4.62
Degree	7	128	80.98	94.00	14,576	MAX VALUE	755.62	39.70	0.49	3.90
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.06%

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

Clustering coefficient 0.54 1.00 0.80 0.74 144.33 0.00 -43.12 0.16 0.19 3.29

Degree 2 66 21.59 7.00 3,886 MAX VALUE 425.96 23.50 1.09 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	0.54	1.00	0.80	0.74	144.33	0.00	-43.12	0.16	0.19	3.29
Degree	2	66	21.59	7.00	3,886	MAX VALUE	425.96	23.50	1.09	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-12-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 13 3.27 2.00 720 MAX VALUE 210.65 2.92 0.89 0.88

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.44 6.00 908 MAX VALUE 261.56 0.83 0.13 0.53

XCSP 2.1 Benchmarks