XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-40-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: 16,320
Value tables: 38

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 4 31 16.04 16.00 261,717 MAX VALUE 44,853.60 3.59 0.22 2.69

Relational linkage 0.05 0.29 0.15 0.15 460.86 0.00 -5,805.67 0.03 0.21 2.35

Tightness 0.79 0.81 0.80 0.80 82.35 0.00 -23.05 0.01 0.01 4.11

Tuples 1,218 1,372 1,283.07 1,282.00 132,156 MAX VALUE 737.13 34.97 0.03 4.11

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

Value table constraints 2 11 5.37 5.00 204 9.54e+25 59.82 2.33 0.43 2.16

Value table partitions 80 80 80.00 80.00 3,040 MAX VALUE 166.52 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	4	31	16.04	16.00	261,717	MAX VALUE	44,853.60	3.59	0.22	2.69
Relational linkage	0.05	0.29	0.15	0.15	460.86	0.00	-5,805.67	0.03	0.21	2.35
Tightness	0.79	0.81	0.80	0.80	82.35	0.00	-23.05	0.01	0.01	4.11
Tuples	1,218	1,372	1,283.07	1,282.00	132,156	MAX VALUE	737.13	34.97	0.03	4.11
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	11	5.37	5.00	204	9.54e+25	59.82	2.33	0.43	2.16
Value table partitions	80	80	80.00	80.00	3,040	MAX VALUE	166.52	0.00	0.00	0.00

Tree decomposition

Number of clusters: 29
Number of leaves: 15
Tree depth: 5
CIR: 0.38
Independent Cluster Pairs: 142
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Tree1.json

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

Cluster constraints 1 16 6.62 5.00 192 3.63e+20 47.34 4.48 0.68 2.34

Variables per cluster 2 12 6.03 5.00 175 9.94e+20 48.35 3.02 0.50 2.20

Separator constraints 0 12 3.07 2.00 89 0 None 3.72 1.21 1.87

Separator variables 0 10 4.66 4.00 135 0 None 2.94 0.63 2.20

Clusters per var 1 15 4.38 3.00 175 6.37e+17 41.00 3.97 0.91 2.01

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	16	6.62	5.00	192	3.63e+20	47.34	4.48	0.68	2.34
Variables per cluster	2	12	6.03	5.00	175	9.94e+20	48.35	3.02	0.50	2.20
Separator constraints	0	12	3.07	2.00	89	0	None	3.72	1.21	1.87
Separator variables	0	10	4.66	4.00	135	0	None	2.94	0.63	2.20
Clusters per var	1	15	4.38	3.00	175	6.37e+17	41.00	3.97	0.91	2.01

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 6
CIR: 0.43
Independent Cluster Pairs: 285
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/DualTree1.json

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

Cluster constraints 6 74 34.71 28.50 1,319 MAX VALUE 127.57 20.02 0.58 3.33

Variables per cluster 4 36 13.92 11.50 529 MAX VALUE 94.73 7.89 0.57 2.84

Separator constraints 0 45 20.26 19.50 770 0 None 12.08 0.60 3.11

Separator variables 0 28 11.21 9.50 426 0 None 6.08 0.54 2.80

Clusters per variable 1 12 5.14 5.00 529 MAX VALUE 145.66 2.83 0.55 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	74	34.71	28.50	1,319	MAX VALUE	127.57	20.02	0.58	3.33
Variables per cluster	4	36	13.92	11.50	529	MAX VALUE	94.73	7.89	0.57	2.84
Separator constraints	0	45	20.26	19.50	770	0	None	12.08	0.60	3.11
Separator variables	0	28	11.21	9.50	426	0	None	6.08	0.54	2.80
Clusters per variable	1	12	5.14	5.00	529	MAX VALUE	145.66	2.83	0.55	2.15

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 64
Triangles: 27
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-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 2.61

Degree 1 11 5.15 5.00 206 9.54e+25 59.82 2.47 0.48 2.25

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.61 4.00 231 2.25e+35 81.40 0.55 0.15 0.80

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	2.61
Degree	1	11	5.15	5.00	206	9.54e+25	59.82	2.47	0.48	2.25
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.61	4.00	231	2.25e+35	81.40	0.55	0.15	0.80

Triangulated primal graph

Density: 25.77%
MCB compute time (ms): 3
MCB cycles: 168
Triangles: 592

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

Clustering coefficient 0.44 1.00 None 0.78 None None None None None 2.86

Degree 1 25 10.05 8.00 402 4.86e+33 77.57 7.38 0.73 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 504 MAX VALUE 184.57 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	1.00	None	0.78	None	None	None	None	None	2.86
Degree	1	25	10.05	8.00	402	4.86e+33	77.57	7.38	0.73	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	504	MAX VALUE	184.57	0.00	0.00	0.00

Dual graph

Density: 10.45%
MCB compute time (ms): 33
MCB cycles: 503
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.54 0.50 55.92 0.00 -64.78 0.11 0.21 3.67

Degree 3 17 10.66 11.00 1,098 MAX VALUE 239.51 2.91 0.27 2.42

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.26 3.00 1,642 MAX VALUE 588.24 0.60 0.18 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.54	0.50	55.92	0.00	-64.78	0.11	0.21	3.67
Degree	3	17	10.66	11.00	1,098	MAX VALUE	239.51	2.91	0.27	2.42
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.26	3.00	1,642	MAX VALUE	588.24	0.60	0.18	0.61

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 13
MCB cycles: 64

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 0.37

Degree 1 5 3.22 3.00 332 MAX VALUE 118.11 0.67 0.21 0.99

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.72 7.00 430 MAX VALUE 120.57 1.32 0.20 1.57

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	0.37
Degree	1	5	3.22	3.00	332	MAX VALUE	118.11	0.67	0.21	0.99
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.72	7.00	430	MAX VALUE	120.57	1.32	0.20	1.57

Triangulated dual graph

Density: 32.80%
Triangles: 17,785

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

Clustering coefficient 0.57 1.00 0.80 0.79 82.05 0.00 -24.54 0.12 0.15 3.94

Degree 3 65 33.46 29.00 3,446 MAX VALUE 335.68 19.78 0.59 3.49

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	0.57	1.00	0.80	0.79	82.05	0.00	-24.54	0.12	0.15	3.94
Degree	3	65	33.46	29.00	3,446	MAX VALUE	335.68	19.78	0.59	3.49
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.56%

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

Clustering coefficient 0.33 1.00 None 0.67 None None None None None 3.10

Degree 1 38 11.79 6.00 1,214 MAX VALUE 205.41 11.23 0.95 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	0.33	1.00	None	0.67	None	None	None	None	None	3.10
Degree	1	38	11.79	6.00	1,214	MAX VALUE	205.41	11.23	0.95	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-2-40-80-103-800-40-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-40-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 0.64

Degree 1 11 2.88 2.00 412 MAX VALUE 131.21 1.92 0.67 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.22 8.00 462 MAX VALUE 125.76 1.10 0.15 0.80

XCSP 2.1 Benchmarks