XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-52-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 21 12.59 13.00 113,288 MAX VALUE 22,607.60 2.48 0.20 2.33

Relational linkage 0.12 0.56 0.36 0.36 361.08 0.00 -1,035.26 0.06 0.18 1.88

Tightness 0.43 0.55 0.50 0.50 89.37 0.00 -126.17 0.02 0.04 3.70

Tuples 282 356 314.69 315.00 56,644 MAX VALUE 1,035.15 12.20 0.04 3.70

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 2.18e+37 85.97 2.61 0.29 2.03

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	12.59	13.00	113,288	MAX VALUE	22,607.60	2.48	0.20	2.33
Relational linkage	0.12	0.56	0.36	0.36	361.08	0.00	-1,035.26	0.06	0.18	1.88
Tightness	0.43	0.55	0.50	0.50	89.37	0.00	-126.17	0.02	0.04	3.70
Tuples	282	356	314.69	315.00	56,644	MAX VALUE	1,035.15	12.20	0.04	3.70
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	2.18e+37	85.97	2.61	0.29	2.03
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: 5
CIR: 0.09
Independent Cluster Pairs: 15
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Tree1.json

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

Cluster constraints 4 58 22.10 17.50 442 2.65e+24 56.23 15.87 0.72 2.79

Variables per cluster 5 21 11.30 9.50 226 1.37e+20 46.36 5.16 0.46 2.39

Separator constraints 0 50 13.10 8.50 262 0 None 13.24 1.01 2.72

Separator variables 0 20 9.30 8.00 186 0 None 5.12 0.55 2.46

Clusters per var 1 13 5.65 6.00 226 1.93e+24 55.92 3.84 0.68 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	58	22.10	17.50	442	2.65e+24	56.23	15.87	0.72	2.79
Variables per cluster	5	21	11.30	9.50	226	1.37e+20	46.36	5.16	0.46	2.39
Separator constraints	0	50	13.10	8.50	262	0	None	13.24	1.01	2.72
Separator variables	0	20	9.30	8.00	186	0	None	5.12	0.55	2.46
Clusters per var	1	13	5.65	6.00	226	1.93e+24	55.92	3.84	0.68	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.24
Independent Cluster Pairs: 159
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/DualTree1.json

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

Cluster constraints 16 342 120.82 102.00 4,591 MAX VALUE 173.77 78.11 0.65 3.56

Variables per cluster 8 83 28.24 22.00 1,073 MAX VALUE 120.58 17.78 0.63 3.21

Separator constraints 0 179 79.34 76.00 3,015 0 None 45.93 0.58 3.56

Separator variables 0 58 23.50 19.50 893 0 None 13.47 0.57 3.27

Clusters per variable 1 10 5.96 7.00 1,073 MAX VALUE 291.03 2.73 0.46 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	342	120.82	102.00	4,591	MAX VALUE	173.77	78.11	0.65	3.56
Variables per cluster	8	83	28.24	22.00	1,073	MAX VALUE	120.58	17.78	0.63	3.21
Separator constraints	0	179	79.34	76.00	3,015	0	None	45.93	0.58	3.56
Separator variables	0	58	23.50	19.50	893	0	None	13.47	0.57	3.27
Clusters per variable	1	10	5.96	7.00	1,073	MAX VALUE	291.03	2.73	0.46	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 156
Triangles: 123
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Primal1.json

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

Clustering coefficient 0.00 0.53 0.23 0.22 9.35 0.00 None 0.09 0.38 3.16

Degree 4 15 9.00 9.00 360 2.18e+37 85.97 2.61 0.29 2.03

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.31 3.00 517 MAX VALUE 185.48 0.46 0.14 0.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.53	0.23	0.22	9.35	0.00	None	0.09	0.38	3.16
Degree	4	15	9.00	9.00	360	2.18e+37	85.97	2.61	0.29	2.03
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.31	3.00	517	MAX VALUE	185.48	0.46	0.14	0.62

Triangulated primal graph

Density: 50.77%
MCB compute time (ms): 10
MCB cycles: 363
Triangles: 2,364

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

Clustering coefficient 0.64 1.00 0.84 0.84 33.46 0.00 -7.50 0.11 0.13 3.09

Degree 4 32 19.80 25.00 792 MAX VALUE 112.31 9.52 0.48 2.76

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,089 MAX VALUE 398.80 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	0.84	33.46	0.00	-7.50	0.11	0.13	3.09
Degree	4	32	19.80	25.00	792	MAX VALUE	112.31	9.52	0.48	2.76
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,089	MAX VALUE	398.80	0.00	0.00	0.00

Dual graph

Density: 9.78%
MCB compute time (ms): 330
MCB cycles: 1,674
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Dual1.json

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

Clustering coefficient 0.43 0.66 0.51 0.50 91.09 0.00 -122.94 0.03 0.06 4.11

Degree 7 25 17.51 18.00 3,152 MAX VALUE 511.18 3.57 0.20 2.63

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,330 MAX VALUE 1,927.42 0.39 0.12 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.66	0.51	0.50	91.09	0.00	-122.94	0.03	0.06	4.11
Degree	7	25	17.51	18.00	3,152	MAX VALUE	511.18	3.57	0.20	2.63
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,330	MAX VALUE	1,927.42	0.39	0.12	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 74
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 6 3.56 3.00 640 MAX VALUE 224.43 0.74 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.82 7.00 962 MAX VALUE 268.79 1.08 0.16 1.45

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	6	3.56	3.00	640	MAX VALUE	224.43	0.74	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.82	7.00	962	MAX VALUE	268.79	1.08	0.16	1.45

Triangulated dual graph

Density: 44.21%
Triangles: 177,662

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

Clustering coefficient 0.69 1.00 0.83 0.80 149.08 0.00 -35.06 0.09 0.11 4.64

Degree 7 127 79.14 93.00 14,246 MAX VALUE 750.03 39.79 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	0.69	1.00	0.83	0.80	149.08	0.00	-35.06	0.09	0.11	4.64
Degree	7	127	79.14	93.00	14,246	MAX VALUE	750.03	39.79	0.50	3.93
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.60%

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

Clustering coefficient 0.51 1.00 0.79 0.74 142.71 0.00 -45.19 0.16 0.20 3.27

Degree 2 64 20.77 7.00 3,738 MAX VALUE 421.78 22.63 1.09 3.16

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	0.79	0.74	142.71	0.00	-45.19	0.16	0.20	3.27
Degree	2	64	20.77	7.00	3,738	MAX VALUE	421.78	22.63	1.09	3.16
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-52-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 210.74 2.92 0.89 0.84

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