XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-10-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 12.53 13.00 112,752 MAX VALUE 22,563.30 2.49 0.20 2.33

Relational linkage 0.16 0.64 0.36 0.36 358.16 0.00 -1,042.89 0.06 0.18 1.86

Tightness 0.43 0.55 0.50 0.50 89.80 0.00 -125.32 0.02 0.04 3.74

Tuples 283 358 313.20 313.00 56,376 MAX VALUE 1,034.28 12.83 0.04 3.74

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

Value table constraints 3 18 9.00 9.00 360 1.98e+37 85.88 2.66 0.30 2.17

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	12.53	13.00	112,752	MAX VALUE	22,563.30	2.49	0.20	2.33
Relational linkage	0.16	0.64	0.36	0.36	358.16	0.00	-1,042.89	0.06	0.18	1.86
Tightness	0.43	0.55	0.50	0.50	89.80	0.00	-125.32	0.02	0.04	3.74
Tuples	283	358	313.20	313.00	56,376	MAX VALUE	1,034.28	12.83	0.04	3.74
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	18	9.00	9.00	360	1.98e+37	85.88	2.66	0.30	2.17
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: 8
Tree depth: 4
CIR: 0.12
Independent Cluster Pairs: 21
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Tree1.json

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

Cluster constraints 4 57 21.65 17.50 433 4.93e+24 56.86 14.38 0.66 2.72

Variables per cluster 4 21 10.90 9.50 218 8.37e+19 45.87 4.60 0.42 2.37

Separator constraints 0 47 12.65 9.00 253 0 None 11.46 0.91 2.79

Separator variables 0 19 8.90 8.00 178 0 None 4.47 0.50 2.37

Clusters per var 1 16 5.45 5.50 218 5.46e+23 54.66 3.79 0.70 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	57	21.65	17.50	433	4.93e+24	56.86	14.38	0.66	2.72
Variables per cluster	4	21	10.90	9.50	218	8.37e+19	45.87	4.60	0.42	2.37
Separator constraints	0	47	12.65	9.00	253	0	None	11.46	0.91	2.79
Separator variables	0	19	8.90	8.00	178	0	None	4.47	0.50	2.37
Clusters per var	1	16	5.45	5.50	218	5.46e+23	54.66	3.79	0.70	2.24

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.23
Independent Cluster Pairs: 154
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/DualTree1.json

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

Cluster constraints 18 393 122.47 101.50 4,654 MAX VALUE 174.13 83.34 0.68 3.56

Variables per cluster 8 86 28.42 21.50 1,080 MAX VALUE 120.68 18.28 0.64 3.35

Separator constraints 0 207 80.87 73.50 3,073 0 None 50.54 0.62 3.53

Separator variables 0 62 23.68 19.00 900 0 None 13.94 0.59 3.17

Clusters per variable 1 11 6.00 7.00 1,080 MAX VALUE 292.20 2.72 0.45 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	18	393	122.47	101.50	4,654	MAX VALUE	174.13	83.34	0.68	3.56
Variables per cluster	8	86	28.42	21.50	1,080	MAX VALUE	120.68	18.28	0.64	3.35
Separator constraints	0	207	80.87	73.50	3,073	0	None	50.54	0.62	3.53
Separator variables	0	62	23.68	19.00	900	0	None	13.94	0.59	3.17
Clusters per variable	1	11	6.00	7.00	1,080	MAX VALUE	292.20	2.72	0.45	2.18

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 218
Triangles: 133
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Primal1.json

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

Clustering coefficient 0.11 0.47 0.26 0.27 10.50 0.00 -55.38 0.07 0.28 3.14

Degree 3 18 9.00 9.00 360 1.98e+37 85.88 2.66 0.30 2.17

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.47 3.00 757 MAX VALUE 269.06 0.51 0.15 0.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.11	0.47	0.26	0.27	10.50	0.00	-55.38	0.07	0.28	3.14
Degree	3	18	9.00	9.00	360	1.98e+37	85.88	2.66	0.30	2.17
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.47	3.00	757	MAX VALUE	269.06	0.51	0.15	0.72

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 7
MCB cycles: 388
Triangles: 2,233

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

Clustering coefficient 0.56 1.00 0.83 0.81 33.25 0.00 -7.81 0.12 0.14 3.16

Degree 3 35 19.40 24.00 776 MAX VALUE 111.47 9.44 0.49 2.76

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.01 3.00 1,167 MAX VALUE 427.12 0.09 0.03 0.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.56	1.00	0.83	0.81	33.25	0.00	-7.81	0.12	0.14	3.16
Degree	3	35	19.40	24.00	776	MAX VALUE	111.47	9.44	0.49	2.76
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.01	3.00	1,167	MAX VALUE	427.12	0.09	0.03	0.05

Dual graph

Density: 9.81%
MCB compute time (ms): 280
MCB cycles: 1,756
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Dual1.json

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

Clustering coefficient 0.45 0.75 0.51 0.50 91.58 0.00 -122.19 0.04 0.08 4.17

Degree 7 29 17.57 17.00 3,162 MAX VALUE 511.77 3.70 0.21 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.19 3.00 5,596 MAX VALUE 2,022.10 0.42 0.13 0.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.75	0.51	0.50	91.58	0.00	-122.19	0.04	0.08	4.17
Degree	7	29	17.57	17.00	3,162	MAX VALUE	511.77	3.70	0.21	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.19	3.00	5,596	MAX VALUE	2,022.10	0.42	0.13	0.51

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 86
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 224.54 0.73 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.81 7.00 960 MAX VALUE 268.31 1.12 0.16 1.46

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	224.54	0.73	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.81	7.00	960	MAX VALUE	268.31	1.12	0.16	1.46

Triangulated dual graph

Density: 45.05%
Triangles: 186,681

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

Clustering coefficient 0.68 1.00 0.83 0.80 149.67 0.00 -34.21 0.09 0.11 4.66

Degree 7 130 80.64 93.00 14,516 MAX VALUE 752.81 40.57 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	0.83	0.80	149.67	0.00	-34.21	0.09	0.11	4.66
Degree	7	130	80.64	93.00	14,516	MAX VALUE	752.81	40.57	0.50	4.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.12%

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

Clustering coefficient 0.51 1.00 0.80 0.75 144.43 0.00 -42.86 0.15 0.19 3.31

Degree 2 64 21.69 7.00 3,904 MAX VALUE 427.02 23.60 1.09 3.07

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	0.80	0.75	144.43	0.00	-42.86	0.15	0.19	3.31
Degree	2	64	21.69	7.00	3,904	MAX VALUE	427.02	23.60	1.09	3.07
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 50
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-10-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 18 3.27 2.00 720 MAX VALUE 210.65 2.93 0.89 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.35 6.00 896 MAX VALUE 259.83 0.76 0.12 0.47

XCSP 2.1 Benchmarks