XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-14-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:23
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 12.51 13.00 112,632 MAX VALUE 22,549.80 2.50 0.20 2.33

Relational linkage 0.16 0.60 0.35 0.36 354.60 0.00 -1,053.49 0.06 0.18 1.88

Tightness 0.45 0.55 0.50 0.50 89.89 0.00 -125.12 0.02 0.04 3.75

Tuples 279 343 312.87 313.00 56,316 MAX VALUE 1,034.10 12.28 0.04 3.75

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

Value table constraints 2 14 9.00 9.00 360 1.55e+37 85.63 2.65 0.29 2.27

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	12.51	13.00	112,632	MAX VALUE	22,549.80	2.50	0.20	2.33
Relational linkage	0.16	0.60	0.35	0.36	354.60	0.00	-1,053.49	0.06	0.18	1.88
Tightness	0.45	0.55	0.50	0.50	89.89	0.00	-125.12	0.02	0.04	3.75
Tuples	279	343	312.87	313.00	56,316	MAX VALUE	1,034.10	12.28	0.04	3.75
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	14	9.00	9.00	360	1.55e+37	85.63	2.65	0.29	2.27
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: 9
Tree depth: 4
CIR: 0.13
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Tree1.json

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

Cluster constraints 2 60 22.65 15.00 453 1.35e+24 55.56 17.13 0.76 2.69

Variables per cluster 3 21 11.35 10.00 227 1.30e+20 46.32 5.15 0.45 2.46

Separator constraints 0 48 13.65 6.50 273 0 None 14.81 1.08 2.62

Separator variables 0 19 9.35 8.00 187 0 None 5.12 0.55 2.46

Clusters per var 1 12 5.67 7.00 227 1.88e+24 55.89 3.74 0.66 2.07

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	60	22.65	15.00	453	1.35e+24	55.56	17.13	0.76	2.69
Variables per cluster	3	21	11.35	10.00	227	1.30e+20	46.32	5.15	0.45	2.46
Separator constraints	0	48	13.65	6.50	273	0	None	14.81	1.08	2.62
Separator variables	0	19	9.35	8.00	187	0	None	5.12	0.55	2.46
Clusters per var	1	12	5.67	7.00	227	1.88e+24	55.89	3.74	0.66	2.07

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 6
CIR: 0.20
Independent Cluster Pairs: 132
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/DualTree1.json

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

Cluster constraints 16 333 122.26 107.50 4,646 MAX VALUE 173.71 80.65 0.66 3.53

Variables per cluster 8 83 28.79 21.50 1,094 MAX VALUE 121.00 18.49 0.64 3.26

Separator constraints 0 192 80.68 77.00 3,066 0 None 47.53 0.59 3.53

Separator variables 0 63 24.05 20.00 914 0 None 14.11 0.59 3.25

Clusters per variable 1 11 6.08 7.00 1,094 MAX VALUE 294.62 2.74 0.45 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	333	122.26	107.50	4,646	MAX VALUE	173.71	80.65	0.66	3.53
Variables per cluster	8	83	28.79	21.50	1,094	MAX VALUE	121.00	18.49	0.64	3.26
Separator constraints	0	192	80.68	77.00	3,066	0	None	47.53	0.59	3.53
Separator variables	0	63	24.05	20.00	914	0	None	14.11	0.59	3.25
Clusters per variable	1	11	6.08	7.00	1,094	MAX VALUE	294.62	2.74	0.45	2.25

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 182
Triangles: 111
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Primal1.json

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

Clustering coefficient 0.00 0.36 0.19 0.20 7.68 0.00 None 0.08 0.44 3.19

Degree 2 14 9.00 9.00 360 1.55e+37 85.63 2.65 0.29 2.27

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.43 3.00 624 MAX VALUE 222.32 0.51 0.15 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.36	0.19	0.20	7.68	0.00	None	0.08	0.44	3.19
Degree	2	14	9.00	9.00	360	1.55e+37	85.63	2.65	0.29	2.27
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.43	3.00	624	MAX VALUE	222.32	0.51	0.15	0.71

Triangulated primal graph

Density: 50.90%
MCB compute time (ms): 16
MCB cycles: 358
Triangles: 2,373

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

Clustering coefficient 0.67 1.00 0.84 0.81 33.44 0.00 -7.51 0.11 0.13 3.11

Degree 2 31 19.85 26.00 794 MAX VALUE 112.11 9.52 0.48 2.68

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,074 MAX VALUE 393.30 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	0.84	0.81	33.44	0.00	-7.51	0.11	0.13	3.11
Degree	2	31	19.85	26.00	794	MAX VALUE	112.11	9.52	0.48	2.68
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,074	MAX VALUE	393.30	0.00	0.00	0.00

Dual graph

Density: 9.81%
MCB compute time (ms): 421
MCB cycles: 1,598
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Dual1.json

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

Clustering coefficient 0.43 0.83 0.50 0.49 90.68 0.00 -123.90 0.04 0.08 4.13

Degree 7 26 17.56 18.00 3,160 MAX VALUE 511.95 3.42 0.19 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.14 3.00 5,016 MAX VALUE 1,819.00 0.36 0.11 0.41

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.83	0.50	0.49	90.68	0.00	-123.90	0.04	0.08	4.13
Degree	7	26	17.56	18.00	3,160	MAX VALUE	511.95	3.42	0.19	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.14	3.00	5,016	MAX VALUE	1,819.00	0.36	0.11	0.41

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 71
MCB cycles: 141

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

Clustering coefficient 0.00 1.00 0.01 0.00 1.50 0.00 None 0.08 9.49 0.10

Degree 2 6 3.56 3.00 640 MAX VALUE 223.93 0.80 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.67 7.00 940 MAX VALUE 265.46 1.07 0.16 1.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.01	0.00	1.50	0.00	None	0.08	9.49	0.10
Degree	2	6	3.56	3.00	640	MAX VALUE	223.93	0.80	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.67	7.00	940	MAX VALUE	265.46	1.07	0.16	1.45

Triangulated dual graph

Density: 45.77%
Triangles: 189,560

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

Clustering coefficient 0.68 1.00 0.83 0.81 149.53 0.00 -34.48 0.09 0.11 4.58

Degree 7 132 81.93 97.00 14,748 MAX VALUE 757.61 40.08 0.49 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	0.68	1.00	0.83	0.81	149.53	0.00	-34.48	0.09	0.11	4.58
Degree	7	132	81.93	97.00	14,748	MAX VALUE	757.61	40.08	0.49	4.05
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.90%

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

Clustering coefficient 0.50 1.00 0.80 0.74 143.91 0.00 -43.67 0.16 0.19 3.30

Degree 2 67 21.30 7.00 3,834 MAX VALUE 421.68 23.40 1.10 3.05

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	0.50	1.00	0.80	0.74	143.91	0.00	-43.67	0.16	0.19	3.30
Degree	2	67	21.30	7.00	3,834	MAX VALUE	421.68	23.40	1.10	3.05
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-2-40-25-180-500-14-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-14-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 14 3.27 2.00 720 MAX VALUE 210.40 2.93 0.89 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.58 6.00 928 MAX VALUE 264.43 0.91 0.14 0.60

XCSP 2.1 Benchmarks