XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-65-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 2 21 12.54 13.00 112,840 MAX VALUE 22,570.80 2.48 0.20 2.33

Relational linkage 0.08 0.56 0.36 0.36 359.40 0.00 -1,039.60 0.06 0.17 1.85

Tightness 0.42 0.55 0.50 0.50 89.73 0.00 -125.45 0.02 0.04 3.64

Tuples 284 363 313.44 314.00 56,420 MAX VALUE 1,034.43 12.38 0.04 3.64

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

Value table constraints 4 13 9.00 9.00 360 2.65e+37 86.17 2.47 0.27 2.17

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	2	21	12.54	13.00	112,840	MAX VALUE	22,570.80	2.48	0.20	2.33
Relational linkage	0.08	0.56	0.36	0.36	359.40	0.00	-1,039.60	0.06	0.17	1.85
Tightness	0.42	0.55	0.50	0.50	89.73	0.00	-125.45	0.02	0.04	3.64
Tuples	284	363	313.44	314.00	56,420	MAX VALUE	1,034.43	12.38	0.04	3.64
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	13	9.00	9.00	360	2.65e+37	86.17	2.47	0.27	2.17
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: 11
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 16
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Tree1.json

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

Cluster constraints 5 53 21.10 18.00 443 7.62e+25 59.59 14.06 0.67 2.91

Variables per cluster 5 20 11.00 10.00 231 1.19e+21 48.53 4.65 0.42 2.28

Separator constraints 0 46 12.52 9.00 263 0 None 12.58 1.00 2.69

Separator variables 0 19 9.10 9.00 191 0 None 4.66 0.51 2.38

Clusters per var 1 13 5.78 6.00 231 4.17e+23 54.39 4.13 0.72 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	53	21.10	18.00	443	7.62e+25	59.59	14.06	0.67	2.91
Variables per cluster	5	20	11.00	10.00	231	1.19e+21	48.53	4.65	0.42	2.28
Separator constraints	0	46	12.52	9.00	263	0	None	12.58	1.00	2.69
Separator variables	0	19	9.10	9.00	191	0	None	4.66	0.51	2.38
Clusters per var	1	13	5.78	6.00	231	4.17e+23	54.39	4.13	0.72	2.17

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 135
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/DualTree1.json

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

Cluster constraints 21 411 127.34 106.00 4,839 MAX VALUE 175.07 90.37 0.71 3.53

Variables per cluster 9 87 29.34 23.00 1,115 MAX VALUE 121.72 19.29 0.66 3.32

Separator constraints 0 213 86.24 79.00 3,277 0 None 54.85 0.64 3.53

Separator variables 0 66 24.61 21.00 935 0 None 14.71 0.60 3.28

Clusters per variable 1 10 6.19 7.00 1,115 MAX VALUE 299.10 2.67 0.43 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	411	127.34	106.00	4,839	MAX VALUE	175.07	90.37	0.71	3.53
Variables per cluster	9	87	29.34	23.00	1,115	MAX VALUE	121.72	19.29	0.66	3.32
Separator constraints	0	213	86.24	79.00	3,277	0	None	54.85	0.64	3.53
Separator variables	0	66	24.61	21.00	935	0	None	14.71	0.60	3.28
Clusters per variable	1	10	6.19	7.00	1,115	MAX VALUE	299.10	2.67	0.43	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 152
Triangles: 107
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Primal1.json

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

Clustering coefficient 0.08 0.40 0.21 0.20 8.55 0.00 -64.17 0.07 0.34 3.01

Degree 4 13 9.00 9.00 360 2.65e+37 86.17 2.47 0.27 2.17

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 510 MAX VALUE 182.52 0.48 0.14 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.08	0.40	0.21	0.20	8.55	0.00	-64.17	0.07	0.34	3.01
Degree	4	13	9.00	9.00	360	2.65e+37	86.17	2.47	0.27	2.17
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	510	MAX VALUE	182.52	0.48	0.14	0.65

Triangulated primal graph

Density: 48.85%
MCB compute time (ms): 9
MCB cycles: 351
Triangles: 2,141

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

Clustering coefficient 0.63 1.00 0.83 0.80 33.22 0.00 -7.89 0.13 0.15 3.03

Degree 4 31 19.05 24.00 762 MAX VALUE 110.76 9.46 0.50 2.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,053 MAX VALUE 385.61 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	0.80	33.22	0.00	-7.89	0.13	0.15	3.03
Degree	4	31	19.05	24.00	762	MAX VALUE	110.76	9.46	0.50	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,053	MAX VALUE	385.61	0.00	0.00	0.00

Dual graph

Density: 9.70%
MCB compute time (ms): 440
MCB cycles: 1,612
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Dual1.json

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

Clustering coefficient 0.45 0.67 0.51 0.50 90.98 0.00 -123.17 0.03 0.07 4.12

Degree 8 23 17.36 17.50 3,124 MAX VALUE 510.57 3.07 0.18 2.48

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.17 3.00 5,110 MAX VALUE 1,849.21 0.39 0.12 0.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.67	0.51	0.50	90.98	0.00	-123.17	0.03	0.07	4.12
Degree	8	23	17.36	17.50	3,124	MAX VALUE	510.57	3.07	0.18	2.48
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.17	3.00	5,110	MAX VALUE	1,849.21	0.39	0.12	0.47

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 71
MCB cycles: 142

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 3.56 4.00 640 MAX VALUE 225.03 0.68 0.19 1.02

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.83 7.00 970 MAX VALUE 270.66 1.14 0.17 1.51

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	3.56	4.00	640	MAX VALUE	225.03	0.68	0.19	1.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.83	7.00	970	MAX VALUE	270.66	1.14	0.17	1.51

Triangulated dual graph

Density: 47.94%
Triangles: 210,971

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

Clustering coefficient 0.72 1.00 0.84 0.83 150.91 0.00 -32.62 0.08 0.10 4.66

Degree 8 132 85.81 105.00 15,446 MAX VALUE 765.67 41.29 0.48 3.66

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	0.72	1.00	0.84	0.83	150.91	0.00	-32.62	0.08	0.10	4.66
Degree	8	132	85.81	105.00	15,446	MAX VALUE	765.67	41.29	0.48	3.66
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.66%

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

Clustering coefficient 0.51 1.00 0.80 0.74 143.99 0.00 -43.55 0.16 0.19 3.32

Degree 2 64 20.87 7.00 3,756 MAX VALUE 422.46 22.99 1.10 3.11

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	0.74	143.99	0.00	-43.55	0.16	0.19	3.32
Degree	2	64	20.87	7.00	3,756	MAX VALUE	422.46	22.99	1.10	3.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 40
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-65-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 210.94 2.90 0.89 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.61 6.00 932 MAX VALUE 265.01 0.92 0.14 0.62

XCSP 2.1 Benchmarks