XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-33-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:39
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 4 39 18.04 18.00 539,020 MAX VALUE 85,638.80 4.05 0.22 2.81

Relational linkage 0.02 0.16 0.08 0.08 530.11 0.00 -17,636.50 0.02 0.20 2.44

Tightness 0.90 0.90 0.90 0.90 75.58 0.00 -8.87 0.00 0.00 4.01

Tuples 3,098 3,351 3,246.92 3,248.00 272,741 MAX VALUE 679.17 53.32 0.02 4.01

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

Value table constraints 2 7 4.37 4.00 166 2.36e+23 53.82 1.40 0.32 1.69

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	4	39	18.04	18.00	539,020	MAX VALUE	85,638.80	4.05	0.22	2.81
Relational linkage	0.02	0.16	0.08	0.08	530.11	0.00	-17,636.50	0.02	0.20	2.44
Tightness	0.90	0.90	0.90	0.90	75.58	0.00	-8.87	0.00	0.00	4.01
Tuples	3,098	3,351	3,246.92	3,248.00	272,741	MAX VALUE	679.17	53.32	0.02	4.01
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	7	4.37	4.00	166	2.36e+23	53.82	1.40	0.32	1.69
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: 29
Number of leaves: 13
Tree depth: 6
CIR: 0.49
Independent Cluster Pairs: 186
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Tree1.json

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

Cluster constraints 1 13 4.45 4.00 129 1.20e+16 37.03 3.11 0.70 2.10

Variables per cluster 2 12 5.86 5.00 170 5.56e+20 47.77 2.91 0.50 2.20

Separator constraints 0 9 1.55 0.00 45 0 None 2.65 1.71 1.29

Separator variables 0 11 4.48 4.00 130 0 None 2.80 0.62 2.24

Clusters per var 1 13 4.25 3.50 170 1.66e+18 41.95 3.52 0.83 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	13	4.45	4.00	129	1.20e+16	37.03	3.11	0.70	2.10
Variables per cluster	2	12	5.86	5.00	170	5.56e+20	47.77	2.91	0.50	2.20
Separator constraints	0	9	1.55	0.00	45	0	None	2.65	1.71	1.29
Separator variables	0	11	4.48	4.00	130	0	None	2.80	0.62	2.24
Clusters per var	1	13	4.25	3.50	170	1.66e+18	41.95	3.52	0.83	2.03

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 6
CIR: 0.49
Independent Cluster Pairs: 325
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/DualTree1.json

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

Cluster constraints 4 31 16.95 15.50 644 MAX VALUE 102.84 7.89 0.47 3.02

Variables per cluster 4 24 10.55 9.00 401 1.20e+37 85.38 5.14 0.49 2.69

Separator constraints 0 22 8.61 7.00 327 0 None 5.23 0.61 2.73

Separator variables 0 18 8.34 7.50 317 0 None 3.99 0.48 2.56

Clusters per variable 1 11 4.77 5.00 401 MAX VALUE 111.80 2.81 0.59 2.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	31	16.95	15.50	644	MAX VALUE	102.84	7.89	0.47	3.02
Variables per cluster	4	24	10.55	9.00	401	1.20e+37	85.38	5.14	0.49	2.69
Separator constraints	0	22	8.61	7.00	327	0	None	5.23	0.61	2.73
Separator variables	0	18	8.34	7.50	317	0	None	3.99	0.48	2.56
Clusters per variable	1	11	4.77	5.00	401	MAX VALUE	111.80	2.81	0.59	2.27

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 45
Triangles: 7
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Primal1.json

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

Clustering coefficient 0.00 0.33 None 0.00 None None None None None 1.60

Degree 1 7 4.20 4.00 168 2.36e+23 53.82 1.55 0.37 1.81

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 4.29 4.00 193 1.43e+28 64.83 0.72 0.17 1.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	None	0.00	None	None	None	None	None	1.60
Degree	1	7	4.20	4.00	168	2.36e+23	53.82	1.55	0.37	1.81
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	4.29	4.00	193	1.43e+28	64.83	0.72	0.17	1.02

Triangulated primal graph

Density: 25.13%
MCB compute time (ms): 2
MCB cycles: 160
Triangles: 560

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

Clustering coefficient 0.49 1.00 None 0.73 None None None None None 2.99

Degree 1 23 9.80 9.00 392 3.63e+33 77.28 7.03 0.72 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 480 MAX VALUE 175.78 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	None	0.73	None	None	None	None	None	2.99
Degree	1	23	9.80	9.00	392	3.63e+33	77.28	7.03	0.72	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	480	MAX VALUE	175.78	0.00	0.00	0.00

Dual graph

Density: 9.09%
MCB compute time (ms): 15
MCB cycles: 265
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.49 0.46 40.88 0.00 -61.90 0.10 0.21 2.63

Degree 3 11 7.55 8.00 634 MAX VALUE 167.00 1.85 0.25 1.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 7 3.51 3.00 929 MAX VALUE 324.86 0.93 0.26 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.49	0.46	40.88	0.00	-61.90	0.10	0.21	2.63
Degree	3	11	7.55	8.00	634	MAX VALUE	167.00	1.85	0.25	1.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	7	3.51	3.00	929	MAX VALUE	324.86	0.93	0.26	0.85

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 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 4 3.05 3.00 256 MAX VALUE 91.67 0.63 0.21 0.95

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.98 7.00 314 2.61e+37 86.15 1.56 0.22 1.54

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	4	3.05	3.00	256	MAX VALUE	91.67	0.63	0.21	0.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.98	7.00	314	2.61e+37	86.15	1.56	0.22	1.54

Triangulated dual graph

Density: 27.31%
Triangles: 6,237

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

Clustering coefficient 0.52 1.00 0.78 0.76 65.21 0.00 -22.61 0.14 0.18 3.91

Degree 3 50 22.67 21.00 1,904 MAX VALUE 241.69 13.74 0.61 3.46

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	0.52	1.00	0.78	0.76	65.21	0.00	-22.61	0.14	0.18	3.91
Degree	3	50	22.67	21.00	1,904	MAX VALUE	241.69	13.74	0.61	3.46
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.53%

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

Clustering coefficient 0.39 1.00 0.74 0.67 62.36 0.00 -28.55 0.21 0.29 2.66

Degree 2 28 9.57 5.00 804 MAX VALUE 154.73 8.75 0.91 2.68

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	0.39	1.00	0.74	0.67	62.36	0.00	-28.55	0.21	0.29	2.66
Degree	2	28	9.57	5.00	804	MAX VALUE	154.73	8.75	0.91	2.68
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-2-40-180-84-900-33-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-33-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 0.58

Degree 1 7 2.71 2.00 336 MAX VALUE 112.04 1.35 0.50 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 8.58 8.00 386 MAX VALUE 96.02 1.44 0.17 1.02

XCSP 2.1 Benchmarks