XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-93-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: 8,975
Value tables: 39

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 12.55 13.00 112,603 MAX VALUE 22,515.30 2.47 0.20 2.32

Relational linkage 0.12 0.60 0.36 0.36 348.68 0.00 -1,018.26 0.06 0.17 1.84

Tightness 0.46 0.54 0.50 0.50 89.67 0.00 -125.56 0.02 0.04 3.72

Tuples 285 338 313.65 314.00 56,457 MAX VALUE 1,034.56 11.97 0.04 3.72

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

Value table constraints 4 15 9.21 9.00 359 8.33e+36 85.01 2.49 0.27 2.23

Value table partitions 25 25 25.00 25.00 975 MAX VALUE 125.54 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	12.55	13.00	112,603	MAX VALUE	22,515.30	2.47	0.20	2.32
Relational linkage	0.12	0.60	0.36	0.36	348.68	0.00	-1,018.26	0.06	0.17	1.84
Tightness	0.46	0.54	0.50	0.50	89.67	0.00	-125.56	0.02	0.04	3.72
Tuples	285	338	313.65	314.00	56,457	MAX VALUE	1,034.56	11.97	0.04	3.72
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.21	9.00	359	8.33e+36	85.01	2.49	0.27	2.23
Value table partitions	25	25	25.00	25.00	975	MAX VALUE	125.54	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 8
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 34
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Tree1.json

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

Cluster constraints 1 63 25.90 18.00 518 1.38e+25 57.89 19.58 0.76 2.79

Variables per cluster 2 21 11.65 10.50 233 1.24e+20 46.27 5.74 0.49 2.53

Separator constraints 0 56 16.90 9.50 338 0 None 17.82 1.05 2.69

Separator variables 0 20 9.65 8.50 193 0 None 5.76 0.60 2.62

Clusters per var 1 11 5.83 6.50 233 8.60e+24 57.41 3.70 0.64 2.06

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	63	25.90	18.00	518	1.38e+25	57.89	19.58	0.76	2.79
Variables per cluster	2	21	11.65	10.50	233	1.24e+20	46.27	5.74	0.49	2.53
Separator constraints	0	56	16.90	9.50	338	0	None	17.82	1.05	2.69
Separator variables	0	20	9.65	8.50	193	0	None	5.76	0.60	2.62
Clusters per var	1	11	5.83	6.50	233	8.60e+24	57.41	3.70	0.64	2.06

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 6
CIR: 0.22
Independent Cluster Pairs: 149
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/DualTree1.json

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

Cluster constraints 17 374 124.84 106.00 4,744 MAX VALUE 173.82 86.24 0.69 3.60

Variables per cluster 7 84 28.45 21.50 1,081 MAX VALUE 120.36 18.39 0.65 3.30

Separator constraints 0 192 82.89 74.00 3,150 0 None 51.71 0.62 3.60

Separator variables 0 60 23.71 19.50 901 0 None 14.04 0.59 3.33

Clusters per variable 1 10 6.01 7.00 1,081 MAX VALUE 293.64 2.66 0.44 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	17	374	124.84	106.00	4,744	MAX VALUE	173.82	86.24	0.69	3.60
Variables per cluster	7	84	28.45	21.50	1,081	MAX VALUE	120.36	18.39	0.65	3.30
Separator constraints	0	192	82.89	74.00	3,150	0	None	51.71	0.62	3.60
Separator variables	0	60	23.71	19.50	901	0	None	14.04	0.59	3.33
Clusters per variable	1	10	6.01	7.00	1,081	MAX VALUE	293.64	2.66	0.44	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 200
Triangles: 138
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Primal1.json

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

Clustering coefficient 0.10 0.50 None 0.28 None None None None None 3.29

Degree 1 15 9.00 9.00 360 8.33e+36 85.01 2.77 0.31 2.29

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.41 3.00 682 MAX VALUE 243.31 0.49 0.14 0.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.50	None	0.28	None	None	None	None	None	3.29
Degree	1	15	9.00	9.00	360	8.33e+36	85.01	2.77	0.31	2.29
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.41	3.00	682	MAX VALUE	243.31	0.49	0.14	0.68

Triangulated primal graph

Density: 51.67%
MCB compute time (ms): 13
MCB cycles: 369
Triangles: 2,497

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

Clustering coefficient 0.67 1.00 None 0.81 None None None None None 3.36

Degree 1 30 20.15 25.50 806 MAX VALUE 112.07 9.64 0.48 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,107 MAX VALUE 405.39 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.67	1.00	None	0.81	None	None	None	None	None	3.36
Degree	1	30	20.15	25.50	806	MAX VALUE	112.07	9.64	0.48	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,107	MAX VALUE	405.39	0.00	0.00	0.00

Dual graph

Density: 9.89%
MCB compute time (ms): 740
MCB cycles: 1,444
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Dual1.json

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

Clustering coefficient 0.44 1.00 0.51 0.50 91.15 0.00 -123.04 0.05 0.09 4.26

Degree 6 26 17.71 18.00 3,188 MAX VALUE 512.91 3.69 0.21 2.65

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.03 3.00 4,379 MAX VALUE 1,599.92 0.18 0.06 0.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	1.00	0.51	0.50	91.15	0.00	-123.04	0.05	0.09	4.26
Degree	6	26	17.71	18.00	3,188	MAX VALUE	512.91	3.69	0.21	2.65
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.03	3.00	4,379	MAX VALUE	1,599.92	0.18	0.06	0.14

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 0.33 0.00 0.00 0.83 0.00 None 0.04 7.99 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.03 0.78 0.22 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.62 7.00 934 MAX VALUE 264.16 1.19 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	0.83	0.00	None	0.04	7.99	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.03	0.78	0.22	1.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.62	7.00	934	MAX VALUE	264.16	1.19	0.18	1.57

Triangulated dual graph

Density: 45.21%
Triangles: 185,990

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

Clustering coefficient 0.68 1.00 0.83 0.81 149.29 0.00 -34.74 0.09 0.11 4.60

Degree 6 133 80.92 90.00 14,566 MAX VALUE 754.16 40.03 0.49 4.00

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	0.81	149.29	0.00	-34.74	0.09	0.11	4.60
Degree	6	133	80.92	90.00	14,566	MAX VALUE	754.16	40.03	0.49	4.00
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.97%

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

Clustering coefficient 0.48 1.00 0.79 0.74 142.17 0.00 -46.23 0.16 0.20 3.23

Degree 2 65 19.63 7.00 3,534 MAX VALUE 413.97 21.73 1.11 3.14

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	0.74	142.17	0.00	-46.23	0.16	0.20	3.23
Degree	2	65	19.63	7.00	3,534	MAX VALUE	413.97	21.73	1.11	3.14
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-2-40-25-180-500-93-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-93-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.37

Degree 1 15 3.27 2.00 720 MAX VALUE 209.78 2.95 0.90 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