XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-27-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 12.48 12.00 112,346 MAX VALUE 22,522.60 2.52 0.20 2.34

Relational linkage 0.12 0.60 0.36 0.36 355.20 0.00 -1,052.73 0.06 0.18 1.89

Tightness 0.44 0.57 0.50 0.50 90.12 0.00 -124.70 0.02 0.04 3.86

Tuples 268 348 312.07 311.00 56,173 MAX VALUE 1,033.60 13.90 0.04 3.86

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 2.07e+37 85.92 2.55 0.28 2.21

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	12.48	12.00	112,346	MAX VALUE	22,522.60	2.52	0.20	2.34
Relational linkage	0.12	0.60	0.36	0.36	355.20	0.00	-1,052.73	0.06	0.18	1.89
Tightness	0.44	0.57	0.50	0.50	90.12	0.00	-124.70	0.02	0.04	3.86
Tuples	268	348	312.07	311.00	56,173	MAX VALUE	1,033.60	13.90	0.04	3.86
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	2.07e+37	85.92	2.55	0.28	2.21
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: 0.14
Independent Cluster Pairs: 24
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Tree1.json

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

Cluster constraints 4 60 22.55 16.00 451 7.95e+24 57.34 16.24 0.72 2.62

Variables per cluster 4 21 10.90 9.00 218 6.33e+19 45.59 5.05 0.46 2.32

Separator constraints 0 56 13.55 7.50 271 0 None 14.14 1.04 2.86

Separator variables 0 20 8.90 8.00 178 0 None 4.93 0.55 2.39

Clusters per var 1 13 5.45 6.50 218 3.66e+23 54.26 3.64 0.67 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	60	22.55	16.00	451	7.95e+24	57.34	16.24	0.72	2.62
Variables per cluster	4	21	10.90	9.00	218	6.33e+19	45.59	5.05	0.46	2.32
Separator constraints	0	56	13.55	7.50	271	0	None	14.14	1.04	2.86
Separator variables	0	20	8.90	8.00	178	0	None	4.93	0.55	2.39
Clusters per var	1	13	5.45	6.50	218	3.66e+23	54.26	3.64	0.67	2.09

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 137
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/DualTree1.json

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

Cluster constraints 32 353 122.13 102.00 4,641 MAX VALUE 175.23 79.43 0.65 3.64

Variables per cluster 10 82 28.58 22.00 1,086 MAX VALUE 121.13 18.14 0.63 3.11

Separator constraints 0 176 80.82 68.00 3,071 0 None 46.65 0.58 3.49

Separator variables 0 62 23.84 19.50 906 0 None 13.80 0.58 3.15

Clusters per variable 1 11 6.03 7.00 1,086 MAX VALUE 293.48 2.70 0.45 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	32	353	122.13	102.00	4,641	MAX VALUE	175.23	79.43	0.65	3.64
Variables per cluster	10	82	28.58	22.00	1,086	MAX VALUE	121.13	18.14	0.63	3.11
Separator constraints	0	176	80.82	68.00	3,071	0	None	46.65	0.58	3.49
Separator variables	0	62	23.84	19.50	906	0	None	13.80	0.58	3.15
Clusters per variable	1	11	6.03	7.00	1,086	MAX VALUE	293.48	2.70	0.45	2.24

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 146
Triangles: 121
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Primal1.json

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

Clustering coefficient 0.14 1.00 0.26 0.24 10.50 0.00 -56.50 0.14 0.51 3.16

Degree 3 15 9.00 9.00 360 2.07e+37 85.92 2.55 0.28 2.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.24 3.00 473 MAX VALUE 170.47 0.43 0.13 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.14	1.00	0.26	0.24	10.50	0.00	-56.50	0.14	0.51	3.16
Degree	3	15	9.00	9.00	360	2.07e+37	85.92	2.55	0.28	2.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.24	3.00	473	MAX VALUE	170.47	0.43	0.13	0.55

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 6
MCB cycles: 414
Triangles: 2,276

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

Clustering coefficient 0.64 1.00 0.84 0.82 33.44 0.00 -7.53 0.11 0.13 3.13

Degree 3 32 19.40 25.50 776 MAX VALUE 111.01 9.59 0.49 2.72

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,242 MAX VALUE 454.82 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.84	0.82	33.44	0.00	-7.53	0.11	0.13	3.13
Degree	3	32	19.40	25.50	776	MAX VALUE	111.01	9.59	0.49	2.72
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,242	MAX VALUE	454.82	0.00	0.00	0.00

Dual graph

Density: 9.75%
MCB compute time (ms): 214
MCB cycles: 2,199
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Dual1.json

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

Clustering coefficient 0.46 0.74 0.51 0.50 91.55 0.00 -122.28 0.04 0.09 4.06

Degree 9 26 17.44 17.50 3,140 MAX VALUE 511.48 3.15 0.18 2.54

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.40 3.00 7,481 MAX VALUE 2,666.93 0.53 0.16 0.75

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.74	0.51	0.50	91.55	0.00	-122.28	0.04	0.09	4.06
Degree	9	26	17.44	17.50	3,140	MAX VALUE	511.48	3.15	0.18	2.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.40	3.00	7,481	MAX VALUE	2,666.93	0.53	0.16	0.75

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 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 5 3.56 4.00 640 MAX VALUE 224.31 0.73 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.70 7.00 945 MAX VALUE 265.61 1.24 0.18 1.58

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	224.31	0.73	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.70	7.00	945	MAX VALUE	265.61	1.24	0.18	1.58

Triangulated dual graph

Density: 45.06%
Triangles: 185,403

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

Clustering coefficient 0.68 1.00 0.83 0.82 149.44 0.00 -34.53 0.09 0.11 4.60

Degree 9 128 80.66 101.00 14,518 MAX VALUE 753.61 40.17 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	0.68	1.00	0.83	0.82	149.44	0.00	-34.53	0.09	0.11	4.60
Degree	9	128	80.66	101.00	14,518	MAX VALUE	753.61	40.17	0.50	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.35%

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

Clustering coefficient 0.48 1.00 0.79 0.75 142.81 0.00 -45.11 0.16 0.20 3.29

Degree 2 63 20.32 6.00 3,658 MAX VALUE 416.87 22.51 1.11 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	0.48	1.00	0.79	0.75	142.81	0.00	-45.11	0.16	0.20	3.29
Degree	2	63	20.32	6.00	3,658	MAX VALUE	416.87	22.51	1.11	3.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-27-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 210.69 2.91 0.89 0.88

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.43 6.00 906 MAX VALUE 261.27 0.82 0.13 0.52

XCSP 2.1 Benchmarks