XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-62-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 4 22 12.50 12.00 112,520 MAX VALUE 22,543.20 2.49 0.20 2.33

Relational linkage 0.16 0.56 0.36 0.36 355.88 0.00 -1,049.06 0.06 0.17 1.85

Tightness 0.45 0.55 0.50 0.50 89.98 0.00 -124.92 0.02 0.04 3.71

Tuples 281 346 312.56 312.50 56,260 MAX VALUE 1,033.94 11.55 0.04 3.71

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 9.00 360 2.32e+37 86.04 2.59 0.29 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	12.50	12.00	112,520	MAX VALUE	22,543.20	2.49	0.20	2.33
Relational linkage	0.16	0.56	0.36	0.36	355.88	0.00	-1,049.06	0.06	0.17	1.85
Tightness	0.45	0.55	0.50	0.50	89.98	0.00	-124.92	0.02	0.04	3.71
Tuples	281	346	312.56	312.50	56,260	MAX VALUE	1,033.94	11.55	0.04	3.71
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	9.00	360	2.32e+37	86.04	2.59	0.29	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: 11
Tree depth: 4
CIR: 0.09
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Tree1.json

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

Cluster constraints 5 48 21.29 17.00 447 9.51e+25 59.82 14.00 0.66 2.69

Variables per cluster 4 20 11.00 10.00 231 1.03e+21 48.38 4.83 0.44 2.11

Separator constraints 0 44 12.71 8.00 267 0 None 12.95 1.02 2.65

Separator variables 0 19 9.10 9.00 191 0 None 4.84 0.53 2.20

Clusters per var 1 13 5.78 6.00 231 2.61e+23 53.92 4.17 0.72 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	48	21.29	17.00	447	9.51e+25	59.82	14.00	0.66	2.69
Variables per cluster	4	20	11.00	10.00	231	1.03e+21	48.38	4.83	0.44	2.11
Separator constraints	0	44	12.71	8.00	267	0	None	12.95	1.02	2.65
Separator variables	0	19	9.10	9.00	191	0	None	4.84	0.53	2.20
Clusters per var	1	13	5.78	6.00	231	2.61e+23	53.92	4.17	0.72	2.24

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 145
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/DualTree1.json

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

Cluster constraints 25 382 124.50 106.00 4,731 MAX VALUE 174.93 85.25 0.68 3.48

Variables per cluster 10 81 28.68 21.50 1,090 MAX VALUE 121.18 18.34 0.64 3.11

Separator constraints 0 210 83.08 79.50 3,157 0 None 51.50 0.62 3.44

Separator variables 0 61 23.95 20.00 910 0 None 13.93 0.58 3.17

Clusters per variable 1 11 6.06 7.00 1,090 MAX VALUE 295.10 2.68 0.44 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	382	124.50	106.00	4,731	MAX VALUE	174.93	85.25	0.68	3.48
Variables per cluster	10	81	28.68	21.50	1,090	MAX VALUE	121.18	18.34	0.64	3.11
Separator constraints	0	210	83.08	79.50	3,157	0	None	51.50	0.62	3.44
Separator variables	0	61	23.95	20.00	910	0	None	13.93	0.58	3.17
Clusters per variable	1	11	6.06	7.00	1,090	MAX VALUE	295.10	2.68	0.44	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 146
Triangles: 120
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Primal1.json

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

Clustering coefficient 0.07 0.67 0.25 0.23 9.92 0.00 -58.89 0.10 0.41 3.25

Degree 3 15 9.00 9.00 360 2.32e+37 86.04 2.59 0.29 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.24 3.00 473 MAX VALUE 170.47 0.43 0.13 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.67	0.25	0.23	9.92	0.00	-58.89	0.10	0.41	3.25
Degree	3	15	9.00	9.00	360	2.32e+37	86.04	2.59	0.29	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.24	3.00	473	MAX VALUE	170.47	0.43	0.13	0.55

Triangulated primal graph

Density: 48.85%
MCB compute time (ms): 8
MCB cycles: 360
Triangles: 2,159

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

Clustering coefficient 0.62 1.00 0.83 0.80 33.39 0.00 -7.69 0.13 0.15 2.94

Degree 3 31 19.05 24.00 762 MAX VALUE 110.45 9.60 0.50 2.80

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,080 MAX VALUE 395.50 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.83	0.80	33.39	0.00	-7.69	0.13	0.15	2.94
Degree	3	31	19.05	24.00	762	MAX VALUE	110.45	9.60	0.50	2.80
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,080	MAX VALUE	395.50	0.00	0.00	0.00

Dual graph

Density: 9.77%
MCB compute time (ms): 225
MCB cycles: 1,855
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Dual1.json

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

Clustering coefficient 0.44 0.78 0.51 0.50 91.54 0.00 -122.19 0.04 0.08 4.31

Degree 9 26 17.49 17.00 3,148 MAX VALUE 511.50 3.41 0.20 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.27 3.00 6,067 MAX VALUE 2,181.25 0.46 0.14 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.78	0.51	0.50	91.54	0.00	-122.19	0.04	0.08	4.31
Degree	9	26	17.49	17.00	3,148	MAX VALUE	511.50	3.41	0.20	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.27	3.00	6,067	MAX VALUE	2,181.25	0.46	0.14	0.61

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 76
MCB cycles: 141

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

Clustering coefficient 0.00 0.10 0.00 0.00 0.27 0.00 None 0.01 7.80 0.10

Degree 2 6 3.56 3.00 640 MAX VALUE 224.06 0.78 0.22 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.66 7.00 939 MAX VALUE 264.97 1.14 0.17 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.10	0.00	0.00	0.27	0.00	None	0.01	7.80	0.10
Degree	2	6	3.56	3.00	640	MAX VALUE	224.06	0.78	0.22	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.66	7.00	939	MAX VALUE	264.97	1.14	0.17	1.48

Triangulated dual graph

Density: 45.63%
Triangles: 189,635

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

Clustering coefficient 0.69 1.00 0.83 0.81 149.58 0.00 -34.35 0.09 0.11 4.69

Degree 9 130 81.68 99.50 14,702 MAX VALUE 756.61 40.26 0.49 3.94

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	149.58	0.00	-34.35	0.09	0.11	4.69
Degree	9	130	81.68	99.50	14,702	MAX VALUE	756.61	40.26	0.49	3.94
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.91%

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

Clustering coefficient 0.51 1.00 0.81 0.75 144.96 0.00 -42.49 0.16 0.20 3.29

Degree 2 66 21.32 7.00 3,838 MAX VALUE 421.38 23.50 1.10 3.02

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	0.81	0.75	144.96	0.00	-42.49	0.16	0.20	3.29
Degree	2	66	21.32	7.00	3,838	MAX VALUE	421.38	23.50	1.10	3.02
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-2-40-25-180-500-62-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-62-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 210.80 2.92 0.89 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.43 6.00 906 MAX VALUE 261.27 0.82 0.13 0.52

XCSP 2.1 Benchmarks