XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-73-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: 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 12.50 12.00 112,472 MAX VALUE 22,534.40 2.52 0.20 2.34

Relational linkage 0.12 0.52 0.35 0.36 353.88 0.00 -1,055.27 0.06 0.17 1.85

Tightness 0.44 0.56 0.50 0.50 90.02 0.00 -124.85 0.02 0.04 3.65

Tuples 274 347 312.42 312.00 56,236 MAX VALUE 1,033.86 11.68 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 5 15 9.00 9.00 360 2.82e+37 86.23 2.57 0.29 2.21

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	12.50	12.00	112,472	MAX VALUE	22,534.40	2.52	0.20	2.34
Relational linkage	0.12	0.52	0.35	0.36	353.88	0.00	-1,055.27	0.06	0.17	1.85
Tightness	0.44	0.56	0.50	0.50	90.02	0.00	-124.85	0.02	0.04	3.65
Tuples	274	347	312.42	312.00	56,236	MAX VALUE	1,033.86	11.68	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	5	15	9.00	9.00	360	2.82e+37	86.23	2.57	0.29	2.21
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: 9
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Tree1.json

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

Cluster constraints 7 50 19.57 15.00 411 4.23e+25 59.01 12.17 0.62 2.62

Variables per cluster 6 20 10.71 10.00 225 1.14e+21 48.49 3.94 0.37 2.23

Separator constraints 0 38 11.00 8.00 231 0 None 9.59 0.87 2.71

Separator variables 0 18 8.81 8.00 185 0 None 3.89 0.44 2.23

Clusters per var 1 18 5.62 5.50 225 3.01e+23 54.06 4.25 0.76 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	50	19.57	15.00	411	4.23e+25	59.01	12.17	0.62	2.62
Variables per cluster	6	20	10.71	10.00	225	1.14e+21	48.49	3.94	0.37	2.23
Separator constraints	0	38	11.00	8.00	231	0	None	9.59	0.87	2.71
Separator variables	0	18	8.81	8.00	185	0	None	3.89	0.44	2.23
Clusters per var	1	18	5.62	5.50	225	3.01e+23	54.06	4.25	0.76	2.29

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.21
Independent Cluster Pairs: 143
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/DualTree1.json

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

Cluster constraints 30 363 121.47 102.00 4,616 MAX VALUE 173.91 82.66 0.68 3.55

Variables per cluster 11 82 28.58 21.00 1,086 MAX VALUE 120.93 18.48 0.65 3.08

Separator constraints 0 212 80.11 72.50 3,044 0 None 49.87 0.62 3.55

Separator variables 0 66 23.84 19.50 906 0 None 14.18 0.59 3.12

Clusters per variable 1 10 6.03 7.00 1,086 MAX VALUE 294.26 2.69 0.45 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	30	363	121.47	102.00	4,616	MAX VALUE	173.91	82.66	0.68	3.55
Variables per cluster	11	82	28.58	21.00	1,086	MAX VALUE	120.93	18.48	0.65	3.08
Separator constraints	0	212	80.11	72.50	3,044	0	None	49.87	0.62	3.55
Separator variables	0	66	23.84	19.50	906	0	None	14.18	0.59	3.12
Clusters per variable	1	10	6.03	7.00	1,086	MAX VALUE	294.26	2.69	0.45	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 148
Triangles: 106
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Primal1.json

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

Clustering coefficient 0.10 0.40 0.21 0.20 8.47 0.00 -64.69 0.08 0.36 3.19

Degree 5 15 9.00 9.00 360 2.82e+37 86.23 2.57 0.29 2.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.34 3.00 495 MAX VALUE 177.27 0.48 0.14 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.40	0.21	0.20	8.47	0.00	-64.69	0.08	0.36	3.19
Degree	5	15	9.00	9.00	360	2.82e+37	86.23	2.57	0.29	2.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.34	3.00	495	MAX VALUE	177.27	0.48	0.14	0.64

Triangulated primal graph

Density: 48.08%
MCB compute time (ms): 11
MCB cycles: 341
Triangles: 2,021

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

Clustering coefficient 0.51 1.00 0.82 0.80 32.96 0.00 -8.28 0.13 0.16 3.06

Degree 5 36 18.75 23.00 750 MAX VALUE 110.65 9.35 0.50 2.87

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,023 MAX VALUE 374.63 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.82	0.80	32.96	0.00	-8.28	0.13	0.16	3.06
Degree	5	36	18.75	23.00	750	MAX VALUE	110.65	9.35	0.50	2.87
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,023	MAX VALUE	374.63	0.00	0.00	0.00

Dual graph

Density: 9.76%
MCB compute time (ms): 385
MCB cycles: 1,571
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Dual1.json

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

Clustering coefficient 0.44 0.64 0.51 0.50 91.47 0.00 -122.19 0.03 0.06 4.19

Degree 10 27 17.47 17.00 3,144 MAX VALUE 511.26 3.43 0.20 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.14 3.00 4,933 MAX VALUE 1,788.37 0.37 0.12 0.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.64	0.51	0.50	91.47	0.00	-122.19	0.03	0.06	4.19
Degree	10	27	17.47	17.00	3,144	MAX VALUE	511.26	3.43	0.20	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.14	3.00	4,933	MAX VALUE	1,788.37	0.37	0.12	0.42

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 79
MCB cycles: 142

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 223.99 0.77 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.77 7.00 962 MAX VALUE 269.26 1.19 0.18 1.57

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	223.99	0.77	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.77	7.00	962	MAX VALUE	269.26	1.19	0.18	1.57

Triangulated dual graph

Density: 45.29%
Triangles: 188,700

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

Clustering coefficient 0.69 1.00 0.83 0.81 149.68 0.00 -34.16 0.09 0.10 4.70

Degree 10 130 81.08 102.00 14,594 MAX VALUE 754.19 40.66 0.50 4.03

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	0.69	1.00	0.83	0.81	149.68	0.00	-34.16	0.09	0.10	4.70
Degree	10	130	81.08	102.00	14,594	MAX VALUE	754.19	40.66	0.50	4.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.27%

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

Clustering coefficient 0.46 1.00 0.79 0.71 142.49 0.00 -45.64 0.16 0.20 3.24

Degree 2 65 20.18 7.00 3,632 MAX VALUE 416.01 22.21 1.10 3.15

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	0.46	1.00	0.79	0.71	142.49	0.00	-45.64	0.16	0.20	3.24
Degree	2	65	20.18	7.00	3,632	MAX VALUE	416.01	22.21	1.10	3.15
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-2-40-25-180-500-73-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-73-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 211.00 2.91 0.89 0.88

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