XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-18-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:24
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 12.57 13.00 113,118 MAX VALUE 22,595.10 2.48 0.20 2.32

Relational linkage 0.16 0.64 0.36 0.36 362.60 0.00 -1,031.08 0.06 0.18 1.89

Tightness 0.44 0.54 0.50 0.50 89.51 0.00 -125.90 0.02 0.04 3.75

Tuples 288 347 314.22 313.50 56,559 MAX VALUE 1,034.87 12.46 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 3 16 9.00 10.00 360 1.12e+37 85.30 2.94 0.33 2.30

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	12.57	13.00	113,118	MAX VALUE	22,595.10	2.48	0.20	2.32
Relational linkage	0.16	0.64	0.36	0.36	362.60	0.00	-1,031.08	0.06	0.18	1.89
Tightness	0.44	0.54	0.50	0.50	89.51	0.00	-125.90	0.02	0.04	3.75
Tuples	288	347	314.22	313.50	56,559	MAX VALUE	1,034.87	12.46	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	3	16	9.00	10.00	360	1.12e+37	85.30	2.94	0.33	2.30
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: 21
Number of leaves: 10
Tree depth: 5
CIR: 0.18
Independent Cluster Pairs: 34
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Tree1.json

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

Cluster constraints 5 59 24.52 14.00 515 9.06e+25 59.77 19.89 0.81 2.85

Variables per cluster 4 20 10.90 10.00 229 3.99e+20 47.44 5.48 0.50 2.20

Separator constraints 0 51 15.95 6.00 335 0 None 18.02 1.13 2.60

Separator variables 0 19 9.00 7.00 189 0 None 5.47 0.61 2.27

Clusters per var 1 13 5.72 6.00 229 1.88e+24 55.89 3.77 0.66 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	59	24.52	14.00	515	9.06e+25	59.77	19.89	0.81	2.85
Variables per cluster	4	20	10.90	10.00	229	3.99e+20	47.44	5.48	0.50	2.20
Separator constraints	0	51	15.95	6.00	335	0	None	18.02	1.13	2.60
Separator variables	0	19	9.00	7.00	189	0	None	5.47	0.61	2.27
Clusters per var	1	13	5.72	6.00	229	1.88e+24	55.89	3.77	0.66	2.17

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 148
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/DualTree1.json

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

Cluster constraints 25 408 130.03 105.50 4,941 MAX VALUE 176.28 91.99 0.71 3.56

Variables per cluster 10 87 28.97 21.50 1,101 MAX VALUE 121.29 19.15 0.66 3.10

Separator constraints 0 224 87.58 71.00 3,328 0 None 56.23 0.64 3.49

Separator variables 0 68 24.24 20.00 921 0 None 14.65 0.60 3.06

Clusters per variable 1 10 6.12 7.00 1,101 MAX VALUE 295.97 2.75 0.45 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	408	130.03	105.50	4,941	MAX VALUE	176.28	91.99	0.71	3.56
Variables per cluster	10	87	28.97	21.50	1,101	MAX VALUE	121.29	19.15	0.66	3.10
Separator constraints	0	224	87.58	71.00	3,328	0	None	56.23	0.64	3.49
Separator variables	0	68	24.24	20.00	921	0	None	14.65	0.60	3.06
Clusters per variable	1	10	6.12	7.00	1,101	MAX VALUE	295.97	2.75	0.45	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 141
Triangles: 132
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Primal1.json

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

Clustering coefficient 0.07 0.67 0.27 0.25 10.68 0.00 -56.45 0.12 0.47 3.16

Degree 3 16 9.00 10.00 360 1.12e+37 85.30 2.94 0.33 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.18 3.00 448 MAX VALUE 162.10 0.38 0.12 0.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.67	0.27	0.25	10.68	0.00	-56.45	0.12	0.47	3.16
Degree	3	16	9.00	10.00	360	1.12e+37	85.30	2.94	0.33	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.18	3.00	448	MAX VALUE	162.10	0.38	0.12	0.47

Triangulated primal graph

Density: 48.59%
MCB compute time (ms): 10
MCB cycles: 347
Triangles: 2,210

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

Clustering coefficient 0.64 1.00 0.84 0.80 33.61 0.00 -7.28 0.11 0.13 2.96

Degree 3 31 18.95 24.00 758 MAX VALUE 109.35 9.58 0.51 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,041 MAX VALUE 381.22 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	0.80	33.61	0.00	-7.28	0.11	0.13	2.96
Degree	3	31	18.95	24.00	758	MAX VALUE	109.35	9.58	0.51	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,041	MAX VALUE	381.22	0.00	0.00	0.00

Dual graph

Density: 10.01%
MCB compute time (ms): 514
MCB cycles: 1,558
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Dual1.json

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

Clustering coefficient 0.44 0.79 0.51 0.50 92.66 0.00 -120.30 0.05 0.10 4.33

Degree 9 27 17.92 18.00 3,226 MAX VALUE 515.30 3.80 0.21 2.70

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.08 3.00 4,792 MAX VALUE 1,745.46 0.27 0.09 0.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.79	0.51	0.50	92.66	0.00	-120.30	0.05	0.10	4.33
Degree	9	27	17.92	18.00	3,226	MAX VALUE	515.30	3.80	0.21	2.70
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.08	3.00	4,792	MAX VALUE	1,745.46	0.27	0.09	0.27

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 77
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 224.47 0.73 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.70 7.00 944 MAX VALUE 266.21 1.05 0.16 1.43

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	224.47	0.73	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.70	7.00	944	MAX VALUE	266.21	1.05	0.16	1.43

Triangulated dual graph

Density: 47.08%
Triangles: 205,518

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

Clustering coefficient 0.71 1.00 0.84 0.82 150.89 0.00 -32.62 0.08 0.10 4.63

Degree 9 132 84.28 104.50 15,170 MAX VALUE 761.15 41.68 0.49 3.88

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	0.82	150.89	0.00	-32.62	0.08	0.10	4.63
Degree	9	132	84.28	104.50	15,170	MAX VALUE	761.15	41.68	0.49	3.88
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.69%

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

Clustering coefficient 0.48 1.00 0.80 0.75 143.53 0.00 -44.23 0.16 0.20 3.27

Degree 2 67 20.93 7.00 3,768 MAX VALUE 421.80 22.89 1.09 3.01

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	0.80	0.75	143.53	0.00	-44.23	0.16	0.20	3.27
Degree	2	67	20.93	7.00	3,768	MAX VALUE	421.80	22.89	1.09	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 40
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-18-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 210.07 2.98 0.91 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.35 6.00 896 MAX VALUE 259.83 0.76 0.12 0.47

XCSP 2.1 Benchmarks