XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-56-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 23 12.51 13.00 112,616 MAX VALUE 22,545.20 2.52 0.20 2.34

Relational linkage 0.12 0.56 0.35 0.36 353.84 0.00 -1,056.08 0.06 0.18 1.87

Tightness 0.44 0.55 0.50 0.50 89.91 0.00 -125.12 0.02 0.04 3.82

Tuples 281 350 312.82 313.00 56,308 MAX VALUE 1,034.05 13.42 0.04 3.82

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

Value table constraints 3 16 9.00 9.00 360 2.07e+37 85.93 2.68 0.30 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	3	23	12.51	13.00	112,616	MAX VALUE	22,545.20	2.52	0.20	2.34
Relational linkage	0.12	0.56	0.35	0.36	353.84	0.00	-1,056.08	0.06	0.18	1.87
Tightness	0.44	0.55	0.50	0.50	89.91	0.00	-125.12	0.02	0.04	3.82
Tuples	281	350	312.82	313.00	56,308	MAX VALUE	1,034.05	13.42	0.04	3.82
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	16	9.00	9.00	360	2.07e+37	85.93	2.68	0.30	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: 10
Tree depth: 5
CIR: 0.13
Independent Cluster Pairs: 24
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Tree1.json

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

Cluster constraints 4 54 21.90 18.00 460 1.55e+26 60.30 14.22 0.65 2.98

Variables per cluster 4 20 11.52 10.00 242 2.53e+21 49.28 4.98 0.43 2.31

Separator constraints 0 43 13.33 11.00 280 0 None 12.62 0.95 2.65

Separator variables 0 19 9.62 9.00 202 0 None 5.08 0.53 2.40

Clusters per var 1 13 6.05 6.00 242 4.48e+24 56.76 4.22 0.70 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	54	21.90	18.00	460	1.55e+26	60.30	14.22	0.65	2.98
Variables per cluster	4	20	11.52	10.00	242	2.53e+21	49.28	4.98	0.43	2.31
Separator constraints	0	43	13.33	11.00	280	0	None	12.62	0.95	2.65
Separator variables	0	19	9.62	9.00	202	0	None	5.08	0.53	2.40
Clusters per var	1	13	6.05	6.00	242	4.48e+24	56.76	4.22	0.70	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.24
Independent Cluster Pairs: 160
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/DualTree1.json

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

Cluster constraints 13 345 121.37 103.50 4,612 MAX VALUE 173.46 81.68 0.67 3.48

Variables per cluster 7 79 28.13 21.00 1,069 MAX VALUE 120.47 17.57 0.62 3.10

Separator constraints 0 187 79.68 69.50 3,028 0 None 48.88 0.61 3.46

Separator variables 0 59 23.39 19.00 889 0 None 13.32 0.57 3.14

Clusters per variable 1 10 5.94 7.00 1,069 MAX VALUE 291.50 2.65 0.45 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	345	121.37	103.50	4,612	MAX VALUE	173.46	81.68	0.67	3.48
Variables per cluster	7	79	28.13	21.00	1,069	MAX VALUE	120.47	17.57	0.62	3.10
Separator constraints	0	187	79.68	69.50	3,028	0	None	48.88	0.61	3.46
Separator variables	0	59	23.39	19.00	889	0	None	13.32	0.57	3.14
Clusters per variable	1	10	5.94	7.00	1,069	MAX VALUE	291.50	2.65	0.45	2.19

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 143
Triangles: 127
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Primal1.json

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

Clustering coefficient 0.13 0.47 0.25 0.24 9.84 0.00 -57.66 0.07 0.28 3.19

Degree 3 16 9.00 9.00 360 2.07e+37 85.93 2.68 0.30 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.23 3.00 462 MAX VALUE 166.59 0.42 0.13 0.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.13	0.47	0.25	0.24	9.84	0.00	-57.66	0.07	0.28	3.19
Degree	3	16	9.00	9.00	360	2.07e+37	85.93	2.68	0.30	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.23	3.00	462	MAX VALUE	166.59	0.42	0.13	0.54

Triangulated primal graph

Density: 50.26%
MCB compute time (ms): 8
MCB cycles: 365
Triangles: 2,282

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

Clustering coefficient 0.66 1.00 0.83 0.82 33.34 0.00 -7.68 0.12 0.14 3.08

Degree 3 31 19.60 23.50 784 MAX VALUE 112.02 9.46 0.48 2.85

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,095 MAX VALUE 400.99 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.66	1.00	0.83	0.82	33.34	0.00	-7.68	0.12	0.14	3.08
Degree	3	31	19.60	23.50	784	MAX VALUE	112.02	9.46	0.48	2.85
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,095	MAX VALUE	400.99	0.00	0.00	0.00

Dual graph

Density: 9.83%
MCB compute time (ms): 336
MCB cycles: 1,596
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Dual1.json

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

Clustering coefficient 0.45 0.76 0.51 0.50 91.24 0.00 -122.80 0.04 0.08 4.33

Degree 6 28 17.60 17.00 3,168 MAX VALUE 511.72 3.82 0.22 2.70

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.13 3.00 4,991 MAX VALUE 1,811.66 0.34 0.11 0.39

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.76	0.51	0.50	91.24	0.00	-122.80	0.04	0.08	4.33
Degree	6	28	17.60	17.00	3,168	MAX VALUE	511.72	3.82	0.22	2.70
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.13	3.00	4,991	MAX VALUE	1,811.66	0.34	0.11	0.39

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 67
MCB cycles: 142

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 223.78 0.80 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.57 7.00 933 MAX VALUE 265.23 1.09 0.17 1.49

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	223.78	0.80	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.57	7.00	933	MAX VALUE	265.23	1.09	0.17	1.49

Triangulated dual graph

Density: 43.71%
Triangles: 172,060

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

Clustering coefficient 0.68 1.00 0.82 0.80 148.22 0.00 -36.12 0.09 0.12 4.66

Degree 6 128 78.24 87.50 14,084 MAX VALUE 748.74 39.10 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	0.68	1.00	0.82	0.80	148.22	0.00	-36.12	0.09	0.12	4.66
Degree	6	128	78.24	87.50	14,084	MAX VALUE	748.74	39.10	0.50	4.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.35%

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

Clustering coefficient 0.53 1.00 0.79 0.73 142.33 0.00 -45.72 0.16 0.20 3.33

Degree 2 64 20.31 7.00 3,656 MAX VALUE 418.59 22.33 1.10 3.11

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	0.53	1.00	0.79	0.73	142.33	0.00	-45.72	0.16	0.20	3.33
Degree	2	64	20.31	7.00	3,656	MAX VALUE	418.59	22.33	1.10	3.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-56-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 16 3.27 2.00 720 MAX VALUE 210.69 2.93 0.90 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.44 6.00 908 MAX VALUE 261.56 0.83 0.13 0.53

XCSP 2.1 Benchmarks