XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-61-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 22 12.51 12.00 112,602 MAX VALUE 22,542.40 2.54 0.20 2.35

Relational linkage 0.12 0.56 0.36 0.36 355.52 0.00 -1,050.74 0.06 0.18 1.86

Tightness 0.44 0.55 0.50 0.50 89.92 0.00 -125.08 0.02 0.04 3.72

Tuples 281 349 312.78 312.00 56,301 MAX VALUE 1,034.04 12.77 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 3 15 9.00 8.00 360 2.13e+37 85.95 2.64 0.29 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	3	22	12.51	12.00	112,602	MAX VALUE	22,542.40	2.54	0.20	2.35
Relational linkage	0.12	0.56	0.36	0.36	355.52	0.00	-1,050.74	0.06	0.18	1.86
Tightness	0.44	0.55	0.50	0.50	89.92	0.00	-125.08	0.02	0.04	3.72
Tuples	281	349	312.78	312.00	56,301	MAX VALUE	1,034.04	12.77	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	3	15	9.00	8.00	360	2.13e+37	85.95	2.64	0.29	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: 4
CIR: 0.08
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Tree1.json

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

Cluster constraints 3 47 21.80 17.00 436 8.39e+24 57.39 12.93 0.59 2.58

Variables per cluster 4 21 11.55 10.00 231 2.35e+20 46.91 4.98 0.43 2.32

Separator constraints 0 35 12.80 8.50 256 0 None 11.32 0.88 2.72

Separator variables 0 19 9.55 8.00 191 0 None 4.99 0.52 2.32

Clusters per var 1 13 5.78 6.00 231 9.41e+23 55.20 4.07 0.70 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	47	21.80	17.00	436	8.39e+24	57.39	12.93	0.59	2.58
Variables per cluster	4	21	11.55	10.00	231	2.35e+20	46.91	4.98	0.43	2.32
Separator constraints	0	35	12.80	8.50	256	0	None	11.32	0.88	2.72
Separator variables	0	19	9.55	8.00	191	0	None	4.99	0.52	2.32
Clusters per var	1	13	5.78	6.00	231	9.41e+23	55.20	4.07	0.70	2.23

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 140
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/DualTree1.json

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

Cluster constraints 24 354 122.74 101.50 4,664 MAX VALUE 175.02 80.90 0.66 3.48

Variables per cluster 9 83 28.61 23.00 1,087 MAX VALUE 121.18 18.13 0.63 3.00

Separator constraints 0 186 81.18 72.50 3,085 0 None 48.04 0.59 3.37

Separator variables 0 63 23.87 19.50 907 0 None 13.75 0.58 3.05

Clusters per variable 1 11 6.04 7.00 1,087 MAX VALUE 294.16 2.69 0.45 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	24	354	122.74	101.50	4,664	MAX VALUE	175.02	80.90	0.66	3.48
Variables per cluster	9	83	28.61	23.00	1,087	MAX VALUE	121.18	18.13	0.63	3.00
Separator constraints	0	186	81.18	72.50	3,085	0	None	48.04	0.59	3.37
Separator variables	0	63	23.87	19.50	907	0	None	13.75	0.58	3.05
Clusters per variable	1	11	6.04	7.00	1,087	MAX VALUE	294.16	2.69	0.45	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 152
Triangles: 123
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Primal1.json

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

Clustering coefficient 0.00 0.67 0.24 0.23 9.55 0.00 None 0.10 0.44 3.11

Degree 3 15 9.00 8.00 360 2.13e+37 85.95 2.64 0.29 1.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.29 3.00 500 MAX VALUE 179.58 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	0.24	0.23	9.55	0.00	None	0.10	0.44	3.11
Degree	3	15	9.00	8.00	360	2.13e+37	85.95	2.64	0.29	1.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.29	3.00	500	MAX VALUE	179.58	0.47	0.14	0.63

Triangulated primal graph

Density: 51.41%
MCB compute time (ms): 12
MCB cycles: 367
Triangles: 2,396

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

Clustering coefficient 0.63 1.00 0.84 0.83 33.62 0.00 -7.36 0.12 0.14 3.01

Degree 3 32 20.05 25.00 802 MAX VALUE 112.80 9.63 0.48 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,101 MAX VALUE 403.19 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.84	0.83	33.62	0.00	-7.36	0.12	0.14	3.01
Degree	3	32	20.05	25.00	802	MAX VALUE	112.80	9.63	0.48	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,101	MAX VALUE	403.19	0.00	0.00	0.00

Dual graph

Density: 9.80%
MCB compute time (ms): 198
MCB cycles: 2,540
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Dual1.json

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

Clustering coefficient 0.45 0.77 0.51 0.50 91.53 0.00 -122.35 0.05 0.09 3.98

Degree 8 28 17.54 17.00 3,158 MAX VALUE 511.95 3.53 0.20 2.57

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.54 3.00 9,001 MAX VALUE 3,173.31 0.65 0.18 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.77	0.51	0.50	91.53	0.00	-122.35	0.05	0.09	3.98
Degree	8	28	17.54	17.00	3,158	MAX VALUE	511.95	3.53	0.20	2.57
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.54	3.00	9,001	MAX VALUE	3,173.31	0.65	0.18	0.91

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 84
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.01 0.00 1.20 0.00 None 0.04 6.02 0.18

Degree 2 5 3.56 3.00 640 MAX VALUE 224.22 0.75 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.74 7.00 950 MAX VALUE 265.98 1.30 0.19 1.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.20	0.00	None	0.04	6.02	0.18
Degree	2	5	3.56	3.00	640	MAX VALUE	224.22	0.75	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.74	7.00	950	MAX VALUE	265.98	1.30	0.19	1.62

Triangulated dual graph

Density: 45.20%
Triangles: 185,558

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

Clustering coefficient 0.69 1.00 0.83 0.81 149.19 0.00 -34.84 0.09 0.11 4.62

Degree 8 130 80.91 97.50 14,564 MAX VALUE 755.05 40.07 0.50 4.09

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	149.19	0.00	-34.84	0.09	0.11	4.62
Degree	8	130	80.91	97.50	14,564	MAX VALUE	755.05	40.07	0.50	4.09
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.81%

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

Clustering coefficient 0.52 1.00 0.80 0.76 144.45 0.00 -42.71 0.15 0.19 3.22

Degree 2 65 21.14 7.00 3,806 MAX VALUE 420.29 23.49 1.11 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	0.52	1.00	0.80	0.76	144.45	0.00	-42.71	0.15	0.19	3.22
Degree	2	65	21.14	7.00	3,806	MAX VALUE	420.29	23.49	1.11	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-61-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 210.72 2.92 0.89 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.45 6.00 910 MAX VALUE 261.84 0.84 0.13 0.54

XCSP 2.1 Benchmarks