XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-79-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 22 12.43 12.00 111,870 MAX VALUE 22,492.50 2.46 0.20 2.32

Relational linkage 0.12 0.52 0.35 0.36 354.68 0.00 -1,052.56 0.06 0.17 1.83

Tightness 0.45 0.55 0.50 0.50 90.50 0.00 -123.88 0.02 0.04 3.65

Tuples 283 345 310.75 310.00 55,935 MAX VALUE 1,032.90 11.28 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 13 9.00 9.00 360 4.28e+37 86.65 2.17 0.24 1.95

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	12.43	12.00	111,870	MAX VALUE	22,492.50	2.46	0.20	2.32
Relational linkage	0.12	0.52	0.35	0.36	354.68	0.00	-1,052.56	0.06	0.17	1.83
Tightness	0.45	0.55	0.50	0.50	90.50	0.00	-123.88	0.02	0.04	3.65
Tuples	283	345	310.75	310.00	55,935	MAX VALUE	1,032.90	11.28	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	13	9.00	9.00	360	4.28e+37	86.65	2.17	0.24	1.95
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: 12
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Tree1.json

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

Cluster constraints 5 55 23.05 17.00 461 3.29e+25 58.76 15.05 0.65 2.58

Variables per cluster 5 21 11.85 9.50 237 4.86e+20 47.63 5.16 0.44 2.25

Separator constraints 0 50 14.05 8.00 281 0 None 14.14 1.01 2.79

Separator variables 0 20 9.85 8.00 197 0 None 5.23 0.53 2.35

Clusters per var 1 12 5.92 7.00 237 1.60e+24 55.73 4.00 0.68 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	55	23.05	17.00	461	3.29e+25	58.76	15.05	0.65	2.58
Variables per cluster	5	21	11.85	9.50	237	4.86e+20	47.63	5.16	0.44	2.25
Separator constraints	0	50	14.05	8.00	281	0	None	14.14	1.01	2.79
Separator variables	0	20	9.85	8.00	197	0	None	5.23	0.53	2.35
Clusters per var	1	12	5.92	7.00	237	1.60e+24	55.73	4.00	0.68	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/DualTree1.json

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

Cluster constraints 27 329 118.21 102.50 4,492 MAX VALUE 174.75 71.90 0.61 3.56

Variables per cluster 10 82 28.47 22.50 1,082 MAX VALUE 121.45 17.43 0.61 3.26

Separator constraints 0 191 77.84 71.00 2,958 0 None 42.45 0.55 3.53

Separator variables 0 58 23.74 20.00 902 0 None 13.16 0.55 3.15

Clusters per variable 1 10 6.01 7.00 1,082 MAX VALUE 292.42 2.71 0.45 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	27	329	118.21	102.50	4,492	MAX VALUE	174.75	71.90	0.61	3.56
Variables per cluster	10	82	28.47	22.50	1,082	MAX VALUE	121.45	17.43	0.61	3.26
Separator constraints	0	191	77.84	71.00	2,958	0	None	42.45	0.55	3.53
Separator variables	0	58	23.74	20.00	902	0	None	13.16	0.55	3.15
Clusters per variable	1	10	6.01	7.00	1,082	MAX VALUE	292.42	2.71	0.45	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 152
Triangles: 113
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Primal1.json

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

Clustering coefficient 0.10 0.40 0.22 0.22 8.96 0.00 -61.88 0.07 0.31 3.16

Degree 4 13 9.00 9.00 360 4.28e+37 86.65 2.17 0.24 1.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.32 3.00 505 MAX VALUE 181.09 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.40	0.22	0.22	8.96	0.00	-61.88	0.07	0.31	3.16
Degree	4	13	9.00	9.00	360	4.28e+37	86.65	2.17	0.24	1.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.32	3.00	505	MAX VALUE	181.09	0.47	0.14	0.63

Triangulated primal graph

Density: 52.18%
MCB compute time (ms): 13
MCB cycles: 368
Triangles: 2,475

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

Clustering coefficient 0.68 1.00 0.84 0.80 33.71 0.00 -7.22 0.12 0.14 2.91

Degree 4 31 20.35 26.00 814 MAX VALUE 113.84 9.63 0.47 2.75

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,104 MAX VALUE 404.29 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	0.80	33.71	0.00	-7.22	0.12	0.14	2.91
Degree	4	31	20.35	26.00	814	MAX VALUE	113.84	9.63	0.47	2.75
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,104	MAX VALUE	404.29	0.00	0.00	0.00

Dual graph

Density: 9.52%
MCB compute time (ms): 388
MCB cycles: 1,509
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Dual1.json

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

Clustering coefficient 0.45 0.66 0.50 0.49 90.14 0.00 -124.76 0.03 0.06 3.91

Degree 9 24 17.04 17.00 3,068 MAX VALUE 507.82 2.87 0.17 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.13 3.00 4,721 MAX VALUE 1,713.55 0.34 0.11 0.39

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.66	0.50	0.49	90.14	0.00	-124.76	0.03	0.06	3.91
Degree	9	24	17.04	17.00	3,068	MAX VALUE	507.82	2.87	0.17	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.13	3.00	4,721	MAX VALUE	1,713.55	0.34	0.11	0.39

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 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 5 3.56 3.00 640 MAX VALUE 224.46 0.74 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.80 7.00 959 MAX VALUE 268.21 1.13 0.17 1.52

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	5	3.56	3.00	640	MAX VALUE	224.46	0.74	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.80	7.00	959	MAX VALUE	268.21	1.13	0.17	1.52

Triangulated dual graph

Density: 44.04%
Triangles: 174,988

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

Clustering coefficient 0.68 1.00 0.83 0.80 148.65 0.00 -35.63 0.10 0.12 4.62

Degree 9 125 78.83 91.00 14,190 MAX VALUE 750.65 39.33 0.50 3.92

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	0.80	148.65	0.00	-35.63	0.10	0.12	4.62
Degree	9	125	78.83	91.00	14,190	MAX VALUE	750.65	39.33	0.50	3.92
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.45%

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

Clustering coefficient 0.54 1.00 0.79 0.74 141.89 0.00 -46.31 0.16 0.20 3.30

Degree 2 66 20.49 7.00 3,688 MAX VALUE 422.67 22.31 1.09 3.10

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	0.54	1.00	0.79	0.74	141.89	0.00	-46.31	0.16	0.20	3.30
Degree	2	66	20.49	7.00	3,688	MAX VALUE	422.67	22.31	1.09	3.10
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-2-40-25-180-500-79-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-79-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 13 3.27 2.00 720 MAX VALUE 211.42 2.85 0.87 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.55 6.00 924 MAX VALUE 263.86 0.89 0.14 0.59

XCSP 2.1 Benchmarks