XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-32-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 4 22 12.49 12.00 112,390 MAX VALUE 22,533.00 2.49 0.20 2.33

Relational linkage 0.16 0.52 0.36 0.36 355.28 0.00 -1,049.52 0.06 0.16 1.79

Tightness 0.45 0.56 0.50 0.50 90.09 0.00 -124.73 0.02 0.04 3.75

Tuples 272 345 312.19 312.00 56,195 MAX VALUE 1,033.71 12.39 0.04 3.75

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

Value table constraints 5 16 9.00 9.00 360 5.45e+37 86.89 2.07 0.23 1.98

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	4	22	12.49	12.00	112,390	MAX VALUE	22,533.00	2.49	0.20	2.33
Relational linkage	0.16	0.52	0.36	0.36	355.28	0.00	-1,049.52	0.06	0.16	1.79
Tightness	0.45	0.56	0.50	0.50	90.09	0.00	-124.73	0.02	0.04	3.75
Tuples	272	345	312.19	312.00	56,195	MAX VALUE	1,033.71	12.39	0.04	3.75
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	16	9.00	9.00	360	5.45e+37	86.89	2.07	0.23	1.98
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: 5
CIR: 0.03
Independent Cluster Pairs: 5
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Tree1.json

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

Cluster constraints 7 46 23.45 16.00 469 1.27e+26 60.11 12.79 0.55 2.60

Variables per cluster 6 21 12.65 10.50 253 2.48e+21 49.26 4.87 0.39 2.45

Separator constraints 0 38 14.45 7.00 289 0 None 12.44 0.86 2.58

Separator variables 0 19 10.65 8.50 213 0 None 5.10 0.48 2.45

Clusters per var 1 14 6.33 6.50 253 3.40e+25 58.79 4.36 0.69 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	46	23.45	16.00	469	1.27e+26	60.11	12.79	0.55	2.60
Variables per cluster	6	21	12.65	10.50	253	2.48e+21	49.26	4.87	0.39	2.45
Separator constraints	0	38	14.45	7.00	289	0	None	12.44	0.86	2.58
Separator variables	0	19	10.65	8.50	213	0	None	5.10	0.48	2.45
Clusters per var	1	14	6.33	6.50	253	3.40e+25	58.79	4.36	0.69	2.38

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-2-40-25-180-500-32-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/DualTree1.json

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

Cluster constraints 25 386 123.87 98.50 4,707 MAX VALUE 175.64 83.92 0.68 3.51

Variables per cluster 10 88 29.39 22.00 1,117 MAX VALUE 122.17 19.06 0.65 3.10

Separator constraints 0 222 83.71 73.00 3,181 0 None 50.36 0.60 3.48

Separator variables 0 64 24.66 19.50 937 0 None 14.52 0.59 3.14

Clusters per variable 1 10 6.21 7.00 1,117 MAX VALUE 298.52 2.71 0.44 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	386	123.87	98.50	4,707	MAX VALUE	175.64	83.92	0.68	3.51
Variables per cluster	10	88	29.39	22.00	1,117	MAX VALUE	122.17	19.06	0.65	3.10
Separator constraints	0	222	83.71	73.00	3,181	0	None	50.36	0.60	3.48
Separator variables	0	64	24.66	19.50	937	0	None	14.52	0.59	3.14
Clusters per variable	1	10	6.21	7.00	1,117	MAX VALUE	298.52	2.71	0.44	2.16

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 159
Triangles: 106
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Primal1.json

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

Clustering coefficient 0.10 0.33 0.22 0.22 8.75 0.00 -62.20 0.05 0.25 2.85

Degree 5 16 9.00 9.00 360 5.45e+37 86.89 2.07 0.23 1.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.35 3.00 533 MAX VALUE 190.79 0.48 0.14 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.33	0.22	0.22	8.75	0.00	-62.20	0.05	0.25	2.85
Degree	5	16	9.00	9.00	360	5.45e+37	86.89	2.07	0.23	1.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.35	3.00	533	MAX VALUE	190.79	0.48	0.14	0.65

Triangulated primal graph

Density: 54.23%
MCB compute time (ms): 12
MCB cycles: 385
Triangles: 2,618

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

Clustering coefficient 0.65 1.00 0.84 0.81 33.55 0.00 -7.42 0.12 0.14 3.11

Degree 5 33 21.15 24.50 846 MAX VALUE 116.33 9.42 0.45 2.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,155 MAX VALUE 422.97 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.84	0.81	33.55	0.00	-7.42	0.12	0.14	3.11
Degree	5	33	21.15	24.50	846	MAX VALUE	116.33	9.42	0.45	2.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,155	MAX VALUE	422.97	0.00	0.00	0.00

Dual graph

Density: 9.47%
MCB compute time (ms): 244
MCB cycles: 1,954
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Dual1.json

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

Clustering coefficient 0.44 0.62 0.50 0.49 89.84 0.00 -125.35 0.03 0.06 3.94

Degree 9 25 16.96 17.00 3,052 MAX VALUE 506.85 2.93 0.17 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.33 3.00 6,516 MAX VALUE 2,331.99 0.52 0.16 0.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.62	0.50	0.49	89.84	0.00	-125.35	0.03	0.06	3.94
Degree	9	25	16.96	17.00	3,052	MAX VALUE	506.85	2.93	0.17	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.33	3.00	6,516	MAX VALUE	2,331.99	0.52	0.16	0.70

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 69
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 3.00 640 MAX VALUE 224.35 0.74 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.71 7.00 946 MAX VALUE 266.34 1.08 0.16 1.44

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	3.00	640	MAX VALUE	224.35	0.74	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.71	7.00	946	MAX VALUE	266.34	1.08	0.16	1.44

Triangulated dual graph

Density: 47.62%
Triangles: 208,141

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

Clustering coefficient 0.71 1.00 0.84 0.81 150.73 0.00 -32.85 0.09 0.10 4.57

Degree 9 133 85.23 92.00 15,342 MAX VALUE 764.65 41.28 0.48 3.78

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	0.84	0.81	150.73	0.00	-32.85	0.09	0.10	4.57
Degree	9	133	85.23	92.00	15,342	MAX VALUE	764.65	41.28	0.48	3.78
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.46%

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

Clustering coefficient 0.51 1.00 0.80 0.75 144.70 0.00 -42.44 0.15 0.19 3.34

Degree 2 66 22.30 8.00 4,014 MAX VALUE 428.36 24.42 1.09 3.07

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	144.70	0.00	-42.44	0.15	0.19	3.34
Degree	2	66	22.30	8.00	4,014	MAX VALUE	428.36	24.42	1.09	3.07
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-2-40-25-180-500-32-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-32-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 16 3.27 2.00 720 MAX VALUE 211.66 2.84 0.87 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.55 6.00 924 MAX VALUE 263.86 0.89 0.14 0.59

XCSP 2.1 Benchmarks