XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-47-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 22 12.49 12.00 112,450 MAX VALUE 22,541.10 2.47 0.20 2.32

Relational linkage 0.12 0.56 0.36 0.36 358.36 0.00 -1,042.25 0.06 0.17 1.85

Tightness 0.45 0.56 0.50 0.50 90.04 0.00 -124.84 0.02 0.04 3.78

Tuples 274 345 312.36 313.00 56,225 MAX VALUE 1,033.80 12.86 0.04 3.78

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 1.79e+37 85.78 2.74 0.30 2.33

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	12.49	12.00	112,450	MAX VALUE	22,541.10	2.47	0.20	2.32
Relational linkage	0.12	0.56	0.36	0.36	358.36	0.00	-1,042.25	0.06	0.17	1.85
Tightness	0.45	0.56	0.50	0.50	90.04	0.00	-124.84	0.02	0.04	3.78
Tuples	274	345	312.36	313.00	56,225	MAX VALUE	1,033.80	12.86	0.04	3.78
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	1.79e+37	85.78	2.74	0.30	2.33
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: 9
Tree depth: 4
CIR: 0.11
Independent Cluster Pairs: 18
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Tree1.json

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

Cluster constraints 4 51 21.35 15.50 427 1.66e+24 55.77 15.50 0.73 2.62

Variables per cluster 4 20 11.05 10.00 221 9.23e+19 45.97 5.01 0.45 2.42

Separator constraints 0 43 12.35 7.50 247 0 None 12.80 1.04 2.65

Separator variables 0 19 9.05 8.50 181 0 None 4.93 0.55 2.58

Clusters per var 1 12 5.53 5.00 221 3.55e+23 54.23 3.88 0.70 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	51	21.35	15.50	427	1.66e+24	55.77	15.50	0.73	2.62
Variables per cluster	4	20	11.05	10.00	221	9.23e+19	45.97	5.01	0.45	2.42
Separator constraints	0	43	12.35	7.50	247	0	None	12.80	1.04	2.65
Separator variables	0	19	9.05	8.50	181	0	None	4.93	0.55	2.58
Clusters per var	1	12	5.53	5.00	221	3.55e+23	54.23	3.88	0.70	2.21

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 6
CIR: 0.21
Independent Cluster Pairs: 140
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/DualTree1.json

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

Cluster constraints 21 339 121.58 104.00 4,620 MAX VALUE 173.77 79.79 0.66 3.56

Variables per cluster 9 83 28.34 22.00 1,077 MAX VALUE 120.72 17.87 0.63 3.27

Separator constraints 0 184 79.74 70.50 3,030 0 None 47.29 0.59 3.56

Separator variables 0 58 23.61 19.00 897 0 None 13.55 0.57 3.21

Clusters per variable 1 12 5.98 7.00 1,077 MAX VALUE 292.15 2.73 0.46 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	339	121.58	104.00	4,620	MAX VALUE	173.77	79.79	0.66	3.56
Variables per cluster	9	83	28.34	22.00	1,077	MAX VALUE	120.72	17.87	0.63	3.27
Separator constraints	0	184	79.74	70.50	3,030	0	None	47.29	0.59	3.56
Separator variables	0	58	23.61	19.00	897	0	None	13.55	0.57	3.21
Clusters per variable	1	12	5.98	7.00	1,077	MAX VALUE	292.15	2.73	0.46	2.22

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 157
Triangles: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Primal1.json

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

Clustering coefficient 0.00 0.67 0.24 0.22 9.50 0.00 None 0.11 0.47 3.26

Degree 3 15 9.00 9.00 360 1.79e+37 85.78 2.74 0.30 2.33

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.32 3.00 522 MAX VALUE 187.09 0.48 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	0.24	0.22	9.50	0.00	None	0.11	0.47	3.26
Degree	3	15	9.00	9.00	360	1.79e+37	85.78	2.74	0.30	2.33
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.32	3.00	522	MAX VALUE	187.09	0.48	0.14	0.66

Triangulated primal graph

Density: 50.00%
MCB compute time (ms): 11
MCB cycles: 353
Triangles: 2,283

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

Clustering coefficient 0.66 1.00 0.84 0.87 33.57 0.00 -7.42 0.12 0.14 3.06

Degree 3 31 19.50 23.50 780 MAX VALUE 111.42 9.60 0.49 2.89

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	0.66	1.00	0.84	0.87	33.57	0.00	-7.42	0.12	0.14	3.06
Degree	3	31	19.50	23.50	780	MAX VALUE	111.42	9.60	0.49	2.89
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: 9.87%
MCB compute time (ms): 432
MCB cycles: 1,605
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Dual1.json

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

Clustering coefficient 0.44 0.76 0.51 0.50 91.48 0.00 -122.34 0.04 0.08 4.31

Degree 8 26 17.67 18.00 3,180 MAX VALUE 512.54 3.72 0.21 2.70

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.13 3.00 5,021 MAX VALUE 1,822.28 0.34 0.11 0.39

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.76	0.51	0.50	91.48	0.00	-122.34	0.04	0.08	4.31
Degree	8	26	17.67	18.00	3,180	MAX VALUE	512.54	3.72	0.21	2.70
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.13	3.00	5,021	MAX VALUE	1,822.28	0.34	0.11	0.39

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 85
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 5 3.56 4.00 640 MAX VALUE 224.98 0.67 0.19 1.01

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.89 7.00 971 MAX VALUE 270.08 1.12 0.16 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	224.98	0.67	0.19	1.01
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.89	7.00	971	MAX VALUE	270.08	1.12	0.16	1.51

Triangulated dual graph

Density: 44.46%
Triangles: 179,215

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

Clustering coefficient 0.67 1.00 0.83 0.81 148.94 0.00 -35.21 0.09 0.11 4.68

Degree 8 128 79.58 86.50 14,324 MAX VALUE 751.32 39.75 0.50 3.93

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	0.81	148.94	0.00	-35.21	0.09	0.11	4.68
Degree	8	128	79.58	86.50	14,324	MAX VALUE	751.32	39.75	0.50	3.93
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.86%

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

Clustering coefficient 0.52 1.00 0.80 0.72 143.92 0.00 -43.65 0.16 0.19 3.23

Degree 2 66 21.23 7.00 3,822 MAX VALUE 422.64 23.21 1.09 3.17

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	0.52	1.00	0.80	0.72	143.92	0.00	-43.65	0.16	0.19	3.23
Degree	2	66	21.23	7.00	3,822	MAX VALUE	422.64	23.21	1.09	3.17
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 44
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-47-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 210.54 2.94 0.90 0.90

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.50 6.00 916 MAX VALUE 262.71 0.86 0.13 0.56

XCSP 2.1 Benchmarks