XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-23-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 21 12.55 13.00 112,968 MAX VALUE 22,583.80 2.46 0.20 2.32

Relational linkage 0.16 0.56 0.36 0.36 358.40 0.00 -1,042.22 0.06 0.17 1.83

Tightness 0.44 0.56 0.50 0.50 89.63 0.00 -125.65 0.02 0.04 3.66

Tuples 277 347 313.80 313.00 56,484 MAX VALUE 1,034.65 11.79 0.04 3.66

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

Value table constraints 5 14 9.00 9.00 360 4.60e+37 86.72 2.13 0.24 2.00

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	21	12.55	13.00	112,968	MAX VALUE	22,583.80	2.46	0.20	2.32
Relational linkage	0.16	0.56	0.36	0.36	358.40	0.00	-1,042.22	0.06	0.17	1.83
Tightness	0.44	0.56	0.50	0.50	89.63	0.00	-125.65	0.02	0.04	3.66
Tuples	277	347	313.80	313.00	56,484	MAX VALUE	1,034.65	11.79	0.04	3.66
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	14	9.00	9.00	360	4.60e+37	86.72	2.13	0.24	2.00
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: 0.11
Independent Cluster Pairs: 19
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Tree1.json

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

Cluster constraints 7 54 21.95 17.50 439 1.81e+25 58.16 13.72 0.63 2.58

Variables per cluster 6 21 11.45 10.00 229 3.07e+20 47.17 4.70 0.41 2.29

Separator constraints 0 43 12.95 10.50 259 0 None 11.95 0.92 2.62

Separator variables 0 19 9.45 9.00 189 0 None 4.68 0.50 2.29

Clusters per var 1 13 5.72 7.00 229 3.07e+24 56.38 3.75 0.65 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	54	21.95	17.50	439	1.81e+25	58.16	13.72	0.63	2.58
Variables per cluster	6	21	11.45	10.00	229	3.07e+20	47.17	4.70	0.41	2.29
Separator constraints	0	43	12.95	10.50	259	0	None	11.95	0.92	2.62
Separator variables	0	19	9.45	9.00	189	0	None	4.68	0.50	2.29
Clusters per var	1	13	5.72	7.00	229	3.07e+24	56.38	3.75	0.65	2.15

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 148
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/DualTree1.json

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

Cluster constraints 32 338 117.21 99.50 4,454 MAX VALUE 174.82 70.39 0.60 3.51

Variables per cluster 11 86 28.37 21.50 1,078 MAX VALUE 121.38 17.54 0.62 3.20

Separator constraints 0 183 76.92 67.00 2,923 0 None 41.76 0.54 3.40

Separator variables 0 61 23.63 19.00 898 0 None 13.30 0.56 3.01

Clusters per variable 1 10 5.99 7.00 1,078 MAX VALUE 291.29 2.76 0.46 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	32	338	117.21	99.50	4,454	MAX VALUE	174.82	70.39	0.60	3.51
Variables per cluster	11	86	28.37	21.50	1,078	MAX VALUE	121.38	17.54	0.62	3.20
Separator constraints	0	183	76.92	67.00	2,923	0	None	41.76	0.54	3.40
Separator variables	0	61	23.63	19.00	898	0	None	13.30	0.56	3.01
Clusters per variable	1	10	5.99	7.00	1,078	MAX VALUE	291.29	2.76	0.46	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 149
Triangles: 113
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Primal1.json

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

Clustering coefficient 0.06 0.52 0.23 0.22 9.21 0.00 -61.61 0.08 0.36 3.20

Degree 5 14 9.00 9.00 360 4.60e+37 86.72 2.13 0.24 2.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.33 3.00 496 MAX VALUE 177.79 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.06	0.52	0.23	0.22	9.21	0.00	-61.61	0.08	0.36	3.20
Degree	5	14	9.00	9.00	360	4.60e+37	86.72	2.13	0.24	2.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.33	3.00	496	MAX VALUE	177.79	0.47	0.14	0.63

Triangulated primal graph

Density: 51.15%
MCB compute time (ms): 9
MCB cycles: 394
Triangles: 2,348

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

Clustering coefficient 0.63 1.00 0.83 0.80 33.31 0.00 -7.69 0.11 0.14 3.13

Degree 5 32 19.95 26.00 798 MAX VALUE 113.36 9.35 0.47 2.60

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,182 MAX VALUE 432.85 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	0.83	0.80	33.31	0.00	-7.69	0.11	0.14	3.13
Degree	5	32	19.95	26.00	798	MAX VALUE	113.36	9.35	0.47	2.60
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,182	MAX VALUE	432.85	0.00	0.00	0.00

Dual graph

Density: 9.50%
MCB compute time (ms): 417
MCB cycles: 1,462
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Dual1.json

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

Clustering coefficient 0.46 0.64 0.50 0.49 90.00 0.00 -125.02 0.03 0.06 4.08

Degree 10 24 17.01 17.00 3,062 MAX VALUE 507.38 2.96 0.17 2.42

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.10 3.00 4,538 MAX VALUE 1,649.51 0.32 0.10 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.64	0.50	0.49	90.00	0.00	-125.02	0.03	0.06	4.08
Degree	10	24	17.01	17.00	3,062	MAX VALUE	507.38	2.96	0.17	2.42
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.10	3.00	4,538	MAX VALUE	1,649.51	0.32	0.10	0.34

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 67
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 6 3.56 3.00 640 MAX VALUE 224.31 0.76 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.67 7.00 941 MAX VALUE 265.31 1.16 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	6	3.56	3.00	640	MAX VALUE	224.31	0.76	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.67	7.00	941	MAX VALUE	265.31	1.16	0.17	1.52

Triangulated dual graph

Density: 43.91%
Triangles: 177,603

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

Clustering coefficient 0.69 1.00 0.83 0.79 149.28 0.00 -34.72 0.09 0.11 4.57

Degree 10 126 78.60 87.00 14,148 MAX VALUE 748.54 40.29 0.51 3.75

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	0.79	149.28	0.00	-34.72	0.09	0.11	4.57
Degree	10	126	78.60	87.00	14,148	MAX VALUE	748.54	40.29	0.51	3.75
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.79%

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

Clustering coefficient 0.47 1.00 0.79 0.75 142.82 0.00 -44.90 0.15 0.19 3.32

Degree 2 66 21.11 7.00 3,800 MAX VALUE 424.00 23.03 1.09 3.16

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	0.47	1.00	0.79	0.75	142.82	0.00	-44.90	0.15	0.19	3.32
Degree	2	66	21.11	7.00	3,800	MAX VALUE	424.00	23.03	1.09	3.16
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-2-40-25-180-500-23-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-23-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 211.49 2.85 0.87 0.84

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