XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-37-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:40
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 84

General features

Coarse blocks: 29,880
Value tables: 38

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

Arity 2 2 2.00 2.00 168 1.93e+25 58.22 0.00 0.00 0.00

Coarse blocks size 5 38 18.07 18.00 540,028 MAX VALUE 85,710.90 4.02 0.22 2.81

Relational linkage 0.03 0.15 0.08 0.08 532.37 0.00 -17,602.90 0.02 0.20 2.43

Tightness 0.90 0.90 0.90 0.90 75.56 0.00 -8.89 0.00 0.00 4.04

Tuples 3,124 3,395 3,254.00 3,248.00 273,336 MAX VALUE 679.35 51.91 0.02 4.04

Values 180 180 180.00 180.00 7,200 MAX VALUE 207.72 0.00 0.00 0.00

Value table constraints 2 8 4.37 4.00 166 1.75e+23 53.52 1.58 0.36 1.67

Value table partitions 180 180 180.00 180.00 6,840 MAX VALUE 197.33 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	168	1.93e+25	58.22	0.00	0.00	0.00
Coarse blocks size	5	38	18.07	18.00	540,028	MAX VALUE	85,710.90	4.02	0.22	2.81
Relational linkage	0.03	0.15	0.08	0.08	532.37	0.00	-17,602.90	0.02	0.20	2.43
Tightness	0.90	0.90	0.90	0.90	75.56	0.00	-8.89	0.00	0.00	4.04
Tuples	3,124	3,395	3,254.00	3,248.00	273,336	MAX VALUE	679.35	51.91	0.02	4.04
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	8	4.37	4.00	166	1.75e+23	53.52	1.58	0.36	1.67
Value table partitions	180	180	180.00	180.00	6,840	MAX VALUE	197.33	0.00	0.00	0.00

Tree decomposition

Number of clusters: 31
Number of leaves: 15
Tree depth: 5
CIR: 0.41
Independent Cluster Pairs: 177
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Tree1.json

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

Cluster constraints 1 8 3.84 3.00 119 3.12e+16 37.98 1.82 0.47 1.89

Variables per cluster 2 10 5.35 5.00 166 2.46e+21 49.25 2.25 0.42 2.04

Separator constraints 0 5 1.13 0.00 35 0 None 1.58 1.40 1.38

Separator variables 0 9 4.06 4.00 126 0 None 2.21 0.54 2.08

Clusters per var 1 15 4.15 2.50 166 4.41e+16 38.33 4.06 0.98 1.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	8	3.84	3.00	119	3.12e+16	37.98	1.82	0.47	1.89
Variables per cluster	2	10	5.35	5.00	166	2.46e+21	49.25	2.25	0.42	2.04
Separator constraints	0	5	1.13	0.00	35	0	None	1.58	1.40	1.38
Separator variables	0	9	4.06	4.00	126	0	None	2.21	0.54	2.08
Clusters per var	1	15	4.15	2.50	166	4.41e+16	38.33	4.06	0.98	1.91

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.50
Independent Cluster Pairs: 330
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/DualTree1.json

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

Cluster constraints 4 40 17.66 16.00 671 MAX VALUE 103.46 9.09 0.51 3.03

Variables per cluster 5 24 10.39 8.50 395 8.38e+36 85.02 5.07 0.49 2.55

Separator constraints 0 22 9.05 9.50 344 0 None 5.69 0.63 2.76

Separator variables 0 17 8.18 7.00 311 0 None 3.89 0.48 2.51

Clusters per variable 1 11 4.70 4.50 395 MAX VALUE 109.85 2.81 0.60 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	40	17.66	16.00	671	MAX VALUE	103.46	9.09	0.51	3.03
Variables per cluster	5	24	10.39	8.50	395	8.38e+36	85.02	5.07	0.49	2.55
Separator constraints	0	22	9.05	9.50	344	0	None	5.69	0.63	2.76
Separator variables	0	17	8.18	7.00	311	0	None	3.89	0.48	2.51
Clusters per variable	1	11	4.70	4.50	395	MAX VALUE	109.85	2.81	0.60	2.26

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 48
Triangles: 12
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.07 None None None None None 1.98

Degree 1 8 4.20 4.00 168 1.75e+23 53.52 1.71 0.41 1.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 4.17 4.00 200 2.09e+29 67.51 0.82 0.20 1.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.07	None	None	None	None	None	1.98
Degree	1	8	4.20	4.00	168	1.75e+23	53.52	1.71	0.41	1.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	4.17	4.00	200	2.09e+29	67.51	0.82	0.20	1.16

Triangulated primal graph

Density: 21.92%
MCB compute time (ms): 2
MCB cycles: 132
Triangles: 389

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

Clustering coefficient 0.39 1.00 None 0.74 None None None None None 2.81

Degree 1 23 8.55 6.00 342 2.22e+31 72.18 6.58 0.77 2.66

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 396 MAX VALUE 145.02 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.39	1.00	None	0.74	None	None	None	None	None	2.81
Degree	1	23	8.55	6.00	342	2.22e+31	72.18	6.58	0.77	2.66
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	396	MAX VALUE	145.02	0.00	0.00	0.00

Dual graph

Density: 9.38%
MCB compute time (ms): 14
MCB cycles: 287
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.51 0.47 42.63 0.00 -58.32 0.10 0.20 2.71

Degree 4 14 7.79 8.00 654 MAX VALUE 169.06 2.19 0.28 2.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.52 3.00 1,009 MAX VALUE 352.46 0.94 0.27 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.51	0.47	42.63	0.00	-58.32	0.10	0.20	2.71
Degree	4	14	7.79	8.00	654	MAX VALUE	169.06	2.19	0.28	2.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.52	3.00	1,009	MAX VALUE	352.46	0.94	0.27	0.86

Minimal dual graph

Density: 3.67%
MCB compute time (ms): 6
MCB cycles: 45

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

Clustering coefficient 0.00 0.33 0.01 0.00 0.67 0.00 None 0.04 5.52 0.18

Degree 2 4 3.05 3.00 256 MAX VALUE 92.26 0.53 0.17 0.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 7.18 7.00 323 9.21e+37 87.42 1.57 0.22 1.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.67	0.00	None	0.04	5.52	0.18
Degree	2	4	3.05	3.00	256	MAX VALUE	92.26	0.53	0.17	0.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	7.18	7.00	323	9.21e+37	87.42	1.57	0.22	1.80

Triangulated dual graph

Density: 26.91%
Triangles: 6,135

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

Clustering coefficient 0.53 1.00 0.78 0.75 65.28 0.00 -22.59 0.14 0.18 3.86

Degree 4 46 22.33 20.00 1,876 MAX VALUE 239.79 13.90 0.62 3.32

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	0.78	0.75	65.28	0.00	-22.59	0.14	0.18	3.86
Degree	4	46	22.33	20.00	1,876	MAX VALUE	239.79	13.90	0.62	3.32
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.19%

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

Clustering coefficient 0.44 1.00 0.75 0.67 62.61 0.00 -28.03 0.21 0.28 2.67

Degree 2 31 10.12 5.00 850 MAX VALUE 159.40 9.21 0.91 2.73

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	0.44	1.00	0.75	0.67	62.61	0.00	-28.03	0.21	0.28	2.67
Degree	2	31	10.12	5.00	850	MAX VALUE	159.40	9.21	0.91	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.20%
MCB compute time (ms): 8
MCB cycles: 45
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-37-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 0.89

Degree 1 8 2.71 2.00 336 MAX VALUE 111.75 1.41 0.52 1.07

Eccentricity None None None None None None None None None None

MCB cycle size 6 12 8.22 8.00 370 MAX VALUE 93.88 1.65 0.20 1.17

XCSP 2.1 Benchmarks