XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-39-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 23 12.56 13.00 112,998 MAX VALUE 22,584.80 2.47 0.20 2.32

Relational linkage 0.12 0.56 0.36 0.36 358.36 0.00 -1,042.59 0.06 0.17 1.86

Tightness 0.45 0.55 0.50 0.50 89.60 0.00 -125.69 0.02 0.04 3.65

Tuples 283 343 313.88 313.00 56,499 MAX VALUE 1,034.70 11.77 0.04 3.65

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

Value table constraints 4 16 9.00 9.00 360 2.61e+37 86.16 2.71 0.30 2.13

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	23	12.56	13.00	112,998	MAX VALUE	22,584.80	2.47	0.20	2.32
Relational linkage	0.12	0.56	0.36	0.36	358.36	0.00	-1,042.59	0.06	0.17	1.86
Tightness	0.45	0.55	0.50	0.50	89.60	0.00	-125.69	0.02	0.04	3.65
Tuples	283	343	313.88	313.00	56,499	MAX VALUE	1,034.70	11.77	0.04	3.65
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	16	9.00	9.00	360	2.61e+37	86.16	2.71	0.30	2.13
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: 19
Number of leaves: 10
Tree depth: 4
CIR: 0.09
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Tree1.json

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

Cluster constraints 5 64 23.58 13.00 448 7.44e+23 54.97 17.26 0.73 2.52

Variables per cluster 5 22 11.89 10.00 226 4.37e+19 45.22 5.24 0.44 2.33

Separator constraints 0 48 14.11 5.00 268 0 None 14.86 1.05 2.60

Separator variables 0 20 9.79 8.00 186 0 None 5.21 0.53 2.33

Clusters per var 1 12 5.65 6.00 226 2.44e+24 56.15 3.60 0.64 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	64	23.58	13.00	448	7.44e+23	54.97	17.26	0.73	2.52
Variables per cluster	5	22	11.89	10.00	226	4.37e+19	45.22	5.24	0.44	2.33
Separator constraints	0	48	14.11	5.00	268	0	None	14.86	1.05	2.60
Separator variables	0	20	9.79	8.00	186	0	None	5.21	0.53	2.33
Clusters per var	1	12	5.65	6.00	226	2.44e+24	56.15	3.60	0.64	2.17

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 129
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/DualTree1.json

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

Cluster constraints 27 425 126.00 90.50 4,788 MAX VALUE 174.14 95.78 0.76 3.46

Variables per cluster 10 87 29.32 22.00 1,114 MAX VALUE 121.52 19.68 0.67 3.16

Separator constraints 0 222 84.24 64.00 3,201 0 None 57.44 0.68 3.49

Separator variables 0 68 24.58 20.00 934 0 None 15.10 0.61 3.20

Clusters per variable 1 11 6.19 7.00 1,114 MAX VALUE 298.82 2.71 0.44 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	27	425	126.00	90.50	4,788	MAX VALUE	174.14	95.78	0.76	3.46
Variables per cluster	10	87	29.32	22.00	1,114	MAX VALUE	121.52	19.68	0.67	3.16
Separator constraints	0	222	84.24	64.00	3,201	0	None	57.44	0.68	3.49
Separator variables	0	68	24.58	20.00	934	0	None	15.10	0.61	3.20
Clusters per variable	1	11	6.19	7.00	1,114	MAX VALUE	298.82	2.71	0.44	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 155
Triangles: 108
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Primal1.json

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

Clustering coefficient 0.05 0.33 0.20 0.20 7.92 0.00 -67.19 0.06 0.31 3.20

Degree 4 16 9.00 9.00 360 2.61e+37 86.16 2.71 0.30 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.37 3.00 523 MAX VALUE 186.97 0.48 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.05	0.33	0.20	0.20	7.92	0.00	-67.19	0.06	0.31	3.20
Degree	4	16	9.00	9.00	360	2.61e+37	86.16	2.71	0.30	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.37	3.00	523	MAX VALUE	186.97	0.48	0.14	0.66

Triangulated primal graph

Density: 53.46%
MCB compute time (ms): 10
MCB cycles: 388
Triangles: 2,615

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

Clustering coefficient 0.68 1.00 0.84 0.82 33.75 0.00 -7.10 0.11 0.13 3.04

Degree 4 32 20.85 26.00 834 MAX VALUE 114.97 9.58 0.46 2.70

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,164 MAX VALUE 426.26 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.68	1.00	0.84	0.82	33.75	0.00	-7.10	0.11	0.13	3.04
Degree	4	32	20.85	26.00	834	MAX VALUE	114.97	9.58	0.46	2.70
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,164	MAX VALUE	426.26	0.00	0.00	0.00

Dual graph

Density: 9.85%
MCB compute time (ms): 273
MCB cycles: 1,873
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Dual1.json

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

Clustering coefficient 0.45 0.68 0.51 0.50 91.28 0.00 -122.69 0.04 0.07 4.23

Degree 9 29 17.63 17.00 3,174 MAX VALUE 511.87 4.01 0.23 2.75

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.23 3.00 6,043 MAX VALUE 2,178.65 0.44 0.14 0.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.68	0.51	0.50	91.28	0.00	-122.69	0.04	0.07	4.23
Degree	9	29	17.63	17.00	3,174	MAX VALUE	511.87	4.01	0.23	2.75
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.23	3.00	6,043	MAX VALUE	2,178.65	0.44	0.14	0.56

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 68
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.37 0.00 None 0.02 7.94 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.59 0.72 0.20 1.07

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.90 7.00 973 MAX VALUE 270.06 1.17 0.17 1.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.37	0.00	None	0.02	7.94	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.59	0.72	0.20	1.07
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.90	7.00	973	MAX VALUE	270.06	1.17	0.17	1.53

Triangulated dual graph

Density: 48.34%
Triangles: 216,124

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

Clustering coefficient 0.69 1.00 0.84 0.83 151.47 0.00 -31.92 0.08 0.10 4.61

Degree 9 139 86.53 103.50 15,576 MAX VALUE 766.84 41.76 0.48 4.05

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	0.84	0.83	151.47	0.00	-31.92	0.08	0.10	4.61
Degree	9	139	86.53	103.50	15,576	MAX VALUE	766.84	41.76	0.48	4.05
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.84%

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

Clustering coefficient 0.51 1.00 0.80 0.75 143.94 0.00 -43.59 0.15 0.19 3.26

Degree 2 63 21.20 7.50 3,816 MAX VALUE 423.74 23.17 1.09 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	0.51	1.00	0.80	0.75	143.94	0.00	-43.59	0.15	0.19	3.26
Degree	2	63	21.20	7.50	3,816	MAX VALUE	423.74	23.17	1.09	3.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-39-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 210.92 2.94 0.90 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.62 6.00 934 MAX VALUE 265.30 0.93 0.14 0.62

XCSP 2.1 Benchmarks