XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-57-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 12.50 12.00 112,486 MAX VALUE 22,542.90 2.47 0.20 2.32

Relational linkage 0.12 0.52 0.36 0.36 356.60 0.00 -1,047.79 0.06 0.17 1.85

Tightness 0.46 0.56 0.50 0.50 90.01 0.00 -124.88 0.02 0.04 3.74

Tuples 274 339 312.46 314.00 56,243 MAX VALUE 1,033.86 12.35 0.04 3.74

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

Value table constraints 4 15 9.00 9.00 360 1.59e+37 85.66 2.91 0.32 2.36

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	12.50	12.00	112,486	MAX VALUE	22,542.90	2.47	0.20	2.32
Relational linkage	0.12	0.52	0.36	0.36	356.60	0.00	-1,047.79	0.06	0.17	1.85
Tightness	0.46	0.56	0.50	0.50	90.01	0.00	-124.88	0.02	0.04	3.74
Tuples	274	339	312.46	314.00	56,243	MAX VALUE	1,033.86	12.35	0.04	3.74
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.00	9.00	360	1.59e+37	85.66	2.91	0.32	2.36
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: 0.12
Independent Cluster Pairs: 20
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Tree1.json

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

Cluster constraints 5 67 23.05 13.00 461 2.09e+24 56.00 19.65 0.85 2.69

Variables per cluster 5 21 10.95 9.00 219 6.85e+19 45.67 5.23 0.48 2.51

Separator constraints 0 57 14.05 5.50 281 0 None 16.79 1.19 2.44

Separator variables 0 19 8.95 7.50 179 0 None 5.12 0.57 2.51

Clusters per var 1 15 5.47 5.00 219 2.21e+23 53.75 3.87 0.71 2.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	67	23.05	13.00	461	2.09e+24	56.00	19.65	0.85	2.69
Variables per cluster	5	21	10.95	9.00	219	6.85e+19	45.67	5.23	0.48	2.51
Separator constraints	0	57	14.05	5.50	281	0	None	16.79	1.19	2.44
Separator variables	0	19	8.95	7.50	179	0	None	5.12	0.57	2.51
Clusters per var	1	15	5.47	5.00	219	2.21e+23	53.75	3.87	0.71	2.27

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 131
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/DualTree1.json

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

Cluster constraints 28 397 126.84 107.50 4,820 MAX VALUE 174.48 89.76 0.71 3.46

Variables per cluster 10 88 28.82 23.50 1,095 MAX VALUE 120.99 18.81 0.65 3.19

Separator constraints 0 198 84.50 82.50 3,211 0 None 53.63 0.63 3.46

Separator variables 0 61 24.08 21.00 915 0 None 14.31 0.59 3.22

Clusters per variable 1 11 6.08 7.00 1,095 MAX VALUE 295.79 2.66 0.44 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	28	397	126.84	107.50	4,820	MAX VALUE	174.48	89.76	0.71	3.46
Variables per cluster	10	88	28.82	23.50	1,095	MAX VALUE	120.99	18.81	0.65	3.19
Separator constraints	0	198	84.50	82.50	3,211	0	None	53.63	0.63	3.46
Separator variables	0	61	24.08	21.00	915	0	None	14.31	0.59	3.22
Clusters per variable	1	11	6.08	7.00	1,095	MAX VALUE	295.79	2.66	0.44	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 166
Triangles: 124
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.23 0.22 9.31 0.00 None 0.09 0.37 3.25

Degree 4 15 9.00 9.00 360 1.59e+37 85.66 2.91 0.32 2.36

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 558 MAX VALUE 199.63 0.48 0.14 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.23	0.22	9.31	0.00	None	0.09	0.37	3.25
Degree	4	15	9.00	9.00	360	1.59e+37	85.66	2.91	0.32	2.36
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	558	MAX VALUE	199.63	0.48	0.14	0.65

Triangulated primal graph

Density: 49.87%
MCB compute time (ms): 13
MCB cycles: 365
Triangles: 2,304

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

Clustering coefficient 0.57 1.00 0.84 0.82 33.78 0.00 -7.17 0.12 0.14 3.08

Degree 4 34 19.45 24.00 778 MAX VALUE 111.05 9.74 0.50 2.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,095 MAX VALUE 400.99 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.57	1.00	0.84	0.82	33.78	0.00	-7.17	0.12	0.14	3.08
Degree	4	34	19.45	24.00	778	MAX VALUE	111.05	9.74	0.50	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,095	MAX VALUE	400.99	0.00	0.00	0.00

Dual graph

Density: 9.99%
MCB compute time (ms): 279
MCB cycles: 1,844
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Dual1.json

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

Clustering coefficient 0.46 0.70 0.51 0.50 92.53 0.00 -120.30 0.04 0.08 4.34

Degree 9 26 17.88 18.00 3,218 MAX VALUE 514.44 3.92 0.22 2.72

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.25 3.00 5,989 MAX VALUE 2,156.15 0.45 0.14 0.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.70	0.51	0.50	92.53	0.00	-120.30	0.04	0.08	4.34
Degree	9	26	17.88	18.00	3,218	MAX VALUE	514.44	3.92	0.22	2.72
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.25	3.00	5,989	MAX VALUE	2,156.15	0.45	0.14	0.59

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 79
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.67 0.00 None 0.03 8.15 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.39 0.75 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.78 7.00 956 MAX VALUE 267.67 1.12 0.17 1.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.67	0.00	None	0.03	8.15	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.39	0.75	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.78	7.00	956	MAX VALUE	267.67	1.12	0.17	1.49

Triangulated dual graph

Density: 46.55%
Triangles: 198,402

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

Clustering coefficient 0.69 1.00 0.83 0.80 150.15 0.00 -33.60 0.09 0.10 4.62

Degree 9 132 83.33 92.50 15,000 MAX VALUE 760.13 40.75 0.49 3.86

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	0.69	1.00	0.83	0.80	150.15	0.00	-33.60	0.09	0.10	4.62
Degree	9	132	83.33	92.50	15,000	MAX VALUE	760.13	40.75	0.49	3.86
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.04%

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

Clustering coefficient 0.51 1.00 0.80 0.75 144.27 0.00 -43.01 0.15 0.19 3.32

Degree 2 65 21.56 7.00 3,880 MAX VALUE 424.92 23.63 1.10 3.10

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	0.75	144.27	0.00	-43.01	0.15	0.19	3.32
Degree	2	65	21.56	7.00	3,880	MAX VALUE	424.92	23.63	1.10	3.10
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-2-40-25-180-500-57-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-57-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 210.42 2.97 0.91 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