XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-7-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:37
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 103

General features

Coarse blocks: 16,400
Value tables: 39

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

Arity 2 2 2.00 2.00 206 1.01e+31 71.39 0.00 0.00 0.00

Coarse blocks size 3 32 15.98 16.00 262,029 MAX VALUE 45,011.80 3.58 0.22 2.69

Relational linkage 0.04 0.31 0.15 0.15 467.88 0.00 -5,986.45 0.03 0.20 2.29

Tightness 0.79 0.81 0.80 0.80 82.43 0.00 -22.95 0.00 0.01 4.09

Tuples 1,206 1,374 1,278.20 1,275.00 131,655 MAX VALUE 736.75 31.92 0.02 4.09

Values 80 80 80.00 80.00 3,200 MAX VALUE 175.28 0.00 0.00 0.00

Value table constraints 2 9 5.26 5.00 205 7.99e+26 61.95 1.88 0.36 1.95

Value table partitions 80 80 80.00 80.00 3,120 MAX VALUE 170.90 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	206	1.01e+31	71.39	0.00	0.00	0.00
Coarse blocks size	3	32	15.98	16.00	262,029	MAX VALUE	45,011.80	3.58	0.22	2.69
Relational linkage	0.04	0.31	0.15	0.15	467.88	0.00	-5,986.45	0.03	0.20	2.29
Tightness	0.79	0.81	0.80	0.80	82.43	0.00	-22.95	0.00	0.01	4.09
Tuples	1,206	1,374	1,278.20	1,275.00	131,655	MAX VALUE	736.75	31.92	0.02	4.09
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	9	5.26	5.00	205	7.99e+26	61.95	1.88	0.36	1.95
Value table partitions	80	80	80.00	80.00	3,120	MAX VALUE	170.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 27
Number of leaves: 13
Tree depth: 5
CIR: 0.43
Independent Cluster Pairs: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Tree1.json

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

Cluster constraints 1 17 6.52 5.00 176 8.83e+18 43.63 4.79 0.74 2.31

Variables per cluster 2 14 6.56 5.00 177 4.69e+20 47.60 3.20 0.49 2.29

Separator constraints 0 13 2.70 1.00 73 0 None 3.85 1.42 1.81

Separator variables 0 12 5.07 4.00 137 0 None 3.02 0.59 2.29

Clusters per var 1 12 4.42 3.00 177 1.79e+19 44.33 3.51 0.79 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	17	6.52	5.00	176	8.83e+18	43.63	4.79	0.74	2.31
Variables per cluster	2	14	6.56	5.00	177	4.69e+20	47.60	3.20	0.49	2.29
Separator constraints	0	13	2.70	1.00	73	0	None	3.85	1.42	1.81
Separator variables	0	12	5.07	4.00	137	0	None	3.02	0.59	2.29
Clusters per var	1	12	4.42	3.00	177	1.79e+19	44.33	3.51	0.79	2.03

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 6
CIR: 0.43
Independent Cluster Pairs: 286
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/DualTree1.json

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

Cluster constraints 7 75 29.97 23.50 1,139 MAX VALUE 120.62 19.79 0.66 3.26

Variables per cluster 5 34 13.42 11.00 510 MAX VALUE 93.34 7.48 0.56 2.71

Separator constraints 0 50 16.68 14.00 634 0 None 12.32 0.74 3.16

Separator variables 0 25 10.71 9.00 407 0 None 5.77 0.54 2.89

Clusters per variable 1 11 4.95 5.00 510 MAX VALUE 142.44 2.76 0.56 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	75	29.97	23.50	1,139	MAX VALUE	120.62	19.79	0.66	3.26
Variables per cluster	5	34	13.42	11.00	510	MAX VALUE	93.34	7.48	0.56	2.71
Separator constraints	0	50	16.68	14.00	634	0	None	12.32	0.74	3.16
Separator variables	0	25	10.71	9.00	407	0	None	5.77	0.54	2.89
Clusters per variable	1	11	4.95	5.00	510	MAX VALUE	142.44	2.76	0.56	2.26

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 66
Triangles: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.14 None None None None None 2.54

Degree 1 9 5.15 5.00 206 7.99e+26 61.95 1.97 0.38 2.02

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.82 4.00 252 8.48e+37 87.33 0.69 0.18 1.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.14	None	None	None	None	None	2.54
Degree	1	9	5.15	5.00	206	7.99e+26	61.95	1.97	0.38	2.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.82	4.00	252	8.48e+37	87.33	0.69	0.18	1.02

Triangulated primal graph

Density: 29.23%
MCB compute time (ms): 3
MCB cycles: 221
Triangles: 766

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

Clustering coefficient 0.40 1.00 None 0.75 None None None None None 3.00

Degree 1 24 11.40 10.00 456 8.18e+36 84.99 7.62 0.67 2.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 663 MAX VALUE 242.79 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	None	0.75	None	None	None	None	None	3.00
Degree	1	24	11.40	10.00	456	8.18e+36	84.99	7.62	0.67	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	663	MAX VALUE	242.79	0.00	0.00	0.00

Dual graph

Density: 9.61%
MCB compute time (ms): 42
MCB cycles: 412
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.50 0.48 51.64 0.00 -72.13 0.08 0.16 3.33

Degree 4 15 9.81 10.00 1,010 MAX VALUE 230.52 2.78 0.28 2.34

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.17 3.00 1,304 MAX VALUE 470.99 0.48 0.15 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.50	0.48	51.64	0.00	-72.13	0.08	0.16	3.33
Degree	4	15	9.81	10.00	1,010	MAX VALUE	230.52	2.78	0.28	2.34
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.17	3.00	1,304	MAX VALUE	470.99	0.48	0.15	0.46

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 12
MCB cycles: 64

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

Clustering coefficient 0.00 0.17 None 0.00 None None None None None 0.19

Degree 1 5 3.22 3.00 332 MAX VALUE 118.13 0.65 0.20 0.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.77 7.00 433 MAX VALUE 121.21 1.20 0.18 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	None	0.00	None	None	None	None	None	0.19
Degree	1	5	3.22	3.00	332	MAX VALUE	118.13	0.65	0.20	0.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.77	7.00	433	MAX VALUE	121.21	1.20	0.18	1.55

Triangulated dual graph

Density: 30.88%
Triangles: 15,606

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

Clustering coefficient 0.55 1.00 0.79 0.78 81.47 0.00 -25.43 0.13 0.16 4.08

Degree 4 65 31.50 30.00 3,244 MAX VALUE 329.39 18.70 0.59 3.58

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	0.55	1.00	0.79	0.78	81.47	0.00	-25.43	0.13	0.16	4.08
Degree	4	65	31.50	30.00	3,244	MAX VALUE	329.39	18.70	0.59	3.58
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.75%

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

Clustering coefficient 0.47 1.00 None 0.69 None None None None None 3.11

Degree 1 37 11.98 5.00 1,234 MAX VALUE 206.19 11.44 0.96 2.83

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	None	0.69	None	None	None	None	None	3.11
Degree	1	37	11.98	5.00	1,234	MAX VALUE	206.19	11.44	0.96	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 14
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-7-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.48

Degree 1 9 2.88 2.00 412 MAX VALUE 133.34 1.76 0.61 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.62 8.00 488 MAX VALUE 128.92 1.41 0.18 1.03

XCSP 2.1 Benchmarks