XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-81-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 12.00 112,478 MAX VALUE 22,536.10 2.50 0.20 2.34

Relational linkage 0.12 0.56 0.35 0.36 353.80 0.00 -1,057.05 0.06 0.18 1.86

Tightness 0.44 0.56 0.50 0.50 90.02 0.00 -124.88 0.02 0.04 3.77

Tuples 276 347 312.44 313.00 56,239 MAX VALUE 1,033.84 12.91 0.04 3.77

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 4.02e+37 86.59 2.19 0.24 2.14

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	112,478	MAX VALUE	22,536.10	2.50	0.20	2.34
Relational linkage	0.12	0.56	0.35	0.36	353.80	0.00	-1,057.05	0.06	0.18	1.86
Tightness	0.44	0.56	0.50	0.50	90.02	0.00	-124.88	0.02	0.04	3.77
Tuples	276	347	312.44	313.00	56,239	MAX VALUE	1,033.84	12.91	0.04	3.77
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	4.02e+37	86.59	2.19	0.24	2.14
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: 18
Number of leaves: 10
Tree depth: 3
CIR: 0.08
Independent Cluster Pairs: 11
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Tree1.json

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

Cluster constraints 6 60 23.28 18.50 419 4.11e+22 52.07 16.34 0.70 2.58

Variables per cluster 5 23 12.11 10.50 218 4.80e+18 43.02 5.56 0.46 2.48

Separator constraints 0 45 13.28 8.00 239 0 None 13.77 1.04 2.74

Separator variables 0 20 9.89 8.50 178 0 None 5.45 0.55 2.48

Clusters per var 1 11 5.45 6.00 218 7.77e+23 55.01 3.43 0.63 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	60	23.28	18.50	419	4.11e+22	52.07	16.34	0.70	2.58
Variables per cluster	5	23	12.11	10.50	218	4.80e+18	43.02	5.56	0.46	2.48
Separator constraints	0	45	13.28	8.00	239	0	None	13.77	1.04	2.74
Separator variables	0	20	9.89	8.50	178	0	None	5.45	0.55	2.48
Clusters per var	1	11	5.45	6.00	218	7.77e+23	55.01	3.43	0.63	2.22

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.17
Independent Cluster Pairs: 116
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/DualTree1.json

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

Cluster constraints 32 355 120.16 103.50 4,566 MAX VALUE 174.91 76.19 0.63 3.53

Variables per cluster 11 84 28.84 22.00 1,096 MAX VALUE 121.70 18.14 0.63 3.19

Separator constraints 0 175 79.74 78.00 3,030 0 None 45.24 0.57 3.40

Separator variables 0 62 24.11 20.00 916 0 None 13.71 0.57 3.14

Clusters per variable 1 10 6.09 7.00 1,096 MAX VALUE 294.82 2.69 0.44 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	32	355	120.16	103.50	4,566	MAX VALUE	174.91	76.19	0.63	3.53
Variables per cluster	11	84	28.84	22.00	1,096	MAX VALUE	121.70	18.14	0.63	3.19
Separator constraints	0	175	79.74	78.00	3,030	0	None	45.24	0.57	3.40
Separator variables	0	62	24.11	20.00	916	0	None	13.71	0.57	3.14
Clusters per variable	1	10	6.09	7.00	1,096	MAX VALUE	294.82	2.69	0.44	2.09

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 165
Triangles: 107
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Primal1.json

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

Clustering coefficient 0.04 0.40 0.21 0.20 8.40 0.00 -66.08 0.08 0.36 3.08

Degree 4 13 9.00 9.00 360 4.02e+37 86.59 2.19 0.24 2.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.42 3.00 564 MAX VALUE 201.12 0.49 0.14 0.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.04	0.40	0.21	0.20	8.40	0.00	-66.08	0.08	0.36	3.08
Degree	4	13	9.00	9.00	360	4.02e+37	86.59	2.19	0.24	2.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.42	3.00	564	MAX VALUE	201.12	0.49	0.14	0.68

Triangulated primal graph

Density: 55.26%
MCB compute time (ms): 10
MCB cycles: 428
Triangles: 2,829

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

Clustering coefficient 0.71 1.00 0.85 0.83 34.09 0.00 -6.68 0.10 0.12 3.08

Degree 4 32 21.55 27.00 862 MAX VALUE 116.31 9.75 0.45 2.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,284 MAX VALUE 470.21 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.85	0.83	34.09	0.00	-6.68	0.10	0.12	3.08
Degree	4	32	21.55	27.00	862	MAX VALUE	116.31	9.75	0.45	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,284	MAX VALUE	470.21	0.00	0.00	0.00

Dual graph

Density: 9.53%
MCB compute time (ms): 354
MCB cycles: 1,571
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Dual1.json

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

Clustering coefficient 0.45 0.67 0.50 0.49 89.73 0.00 -125.60 0.03 0.06 4.02

Degree 10 23 17.07 17.00 3,072 MAX VALUE 507.77 2.98 0.17 2.44

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.16 3.00 4,971 MAX VALUE 1,799.30 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	0.50	0.49	89.73	0.00	-125.60	0.03	0.06	4.02
Degree	10	23	17.07	17.00	3,072	MAX VALUE	507.77	2.98	0.17	2.44
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.16	3.00	4,971	MAX VALUE	1,799.30	0.39	0.12	0.47

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 76
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 0.53 0.00 None 0.03 9.05 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.17 0.75 0.21 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.67 7.00 941 MAX VALUE 264.93 1.23 0.18 1.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.53	0.00	None	0.03	9.05	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.17	0.75	0.21	1.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.67	7.00	941	MAX VALUE	264.93	1.23	0.18	1.57

Triangulated dual graph

Density: 45.67%
Triangles: 190,369

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

Clustering coefficient 0.71 1.00 0.83 0.81 149.69 0.00 -34.20 0.09 0.11 4.59

Degree 10 126 81.74 99.00 14,714 MAX VALUE 756.67 40.43 0.49 3.70

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	0.71	1.00	0.83	0.81	149.69	0.00	-34.20	0.09	0.11	4.59
Degree	10	126	81.74	99.00	14,714	MAX VALUE	756.67	40.43	0.49	3.70
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.87%

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

Clustering coefficient 0.53 1.00 0.80 0.75 143.82 0.00 -43.43 0.15 0.19 3.29

Degree 2 65 21.26 7.00 3,826 MAX VALUE 420.95 23.59 1.11 3.03

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	0.53	1.00	0.80	0.75	143.82	0.00	-43.43	0.15	0.19	3.29
Degree	2	65	21.26	7.00	3,826	MAX VALUE	420.95	23.59	1.11	3.03
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-2-40-25-180-500-81-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-81-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 211.35 2.86 0.87 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.64 6.00 936 MAX VALUE 265.58 0.93 0.14 0.63

XCSP 2.1 Benchmarks