XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-98-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 3 23 12.46 12.00 112,096 MAX VALUE 22,507.20 2.48 0.20 2.33

Relational linkage 0.12 0.64 0.35 0.36 353.60 0.00 -1,057.52 0.07 0.18 1.90

Tightness 0.44 0.55 0.50 0.50 90.32 0.00 -124.27 0.02 0.04 3.77

Tuples 279 347 311.38 311.50 56,048 MAX VALUE 1,033.23 12.58 0.04 3.77

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

Value table constraints 2 14 9.00 9.00 360 1.02e+37 85.22 2.78 0.31 2.25

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	3	23	12.46	12.00	112,096	MAX VALUE	22,507.20	2.48	0.20	2.33
Relational linkage	0.12	0.64	0.35	0.36	353.60	0.00	-1,057.52	0.07	0.18	1.90
Tightness	0.44	0.55	0.50	0.50	90.32	0.00	-124.27	0.02	0.04	3.77
Tuples	279	347	311.38	311.50	56,048	MAX VALUE	1,033.23	12.58	0.04	3.77
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	14	9.00	9.00	360	1.02e+37	85.22	2.78	0.31	2.25
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: 11
Tree depth: 4
CIR: 0.16
Independent Cluster Pairs: 27
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Tree1.json

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

Cluster constraints 2 57 21.50 18.00 430 7.07e+23 54.92 15.78 0.73 2.93

Variables per cluster 3 21 10.70 9.00 214 2.51e+19 44.67 5.34 0.50 2.62

Separator constraints 0 47 12.50 8.50 250 0 None 12.77 1.02 2.86

Separator variables 0 19 8.70 8.00 174 0 None 5.19 0.60 2.62

Clusters per var 1 12 5.35 5.50 214 1.42e+23 53.31 3.55 0.66 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	57	21.50	18.00	430	7.07e+23	54.92	15.78	0.73	2.93
Variables per cluster	3	21	10.70	9.00	214	2.51e+19	44.67	5.34	0.50	2.62
Separator constraints	0	47	12.50	8.50	250	0	None	12.77	1.02	2.86
Separator variables	0	19	8.70	8.00	174	0	None	5.19	0.60	2.62
Clusters per var	1	12	5.35	5.50	214	1.42e+23	53.31	3.55	0.66	2.15

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 6
CIR: 0.21
Independent Cluster Pairs: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/DualTree1.json

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

Cluster constraints 29 332 125.16 100.00 4,756 MAX VALUE 175.72 81.79 0.65 3.53

Variables per cluster 9 80 28.84 21.00 1,096 MAX VALUE 121.25 18.50 0.64 3.11

Separator constraints 0 184 83.18 70.00 3,161 0 None 48.19 0.58 3.60

Separator variables 0 62 24.11 19.50 916 0 None 14.18 0.59 3.22

Clusters per variable 1 11 6.09 7.00 1,096 MAX VALUE 295.18 2.72 0.45 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	29	332	125.16	100.00	4,756	MAX VALUE	175.72	81.79	0.65	3.53
Variables per cluster	9	80	28.84	21.00	1,096	MAX VALUE	121.25	18.50	0.64	3.11
Separator constraints	0	184	83.18	70.00	3,161	0	None	48.19	0.58	3.60
Separator variables	0	62	24.11	19.50	916	0	None	14.18	0.59	3.22
Clusters per variable	1	11	6.09	7.00	1,096	MAX VALUE	295.18	2.72	0.45	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 146
Triangles: 134
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Primal1.json

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

Clustering coefficient 0.00 0.39 0.25 0.27 10.13 0.00 None 0.08 0.30 3.23

Degree 2 14 9.00 9.00 360 1.02e+37 85.22 2.78 0.31 2.25

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.19 3.00 466 MAX VALUE 168.45 0.39 0.12 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.39	0.25	0.27	10.13	0.00	None	0.08	0.30	3.23
Degree	2	14	9.00	9.00	360	1.02e+37	85.22	2.78	0.31	2.25
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.19	3.00	466	MAX VALUE	168.45	0.39	0.12	0.49

Triangulated primal graph

Density: 49.23%
MCB compute time (ms): 11
MCB cycles: 346
Triangles: 2,269

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

Clustering coefficient 0.66 1.00 0.84 0.82 33.74 0.00 -7.15 0.11 0.13 2.99

Degree 2 31 19.20 24.50 768 MAX VALUE 109.56 9.71 0.51 2.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,038 MAX VALUE 380.12 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.66	1.00	0.84	0.82	33.74	0.00	-7.15	0.11	0.13	2.99
Degree	2	31	19.20	24.50	768	MAX VALUE	109.56	9.71	0.51	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,038	MAX VALUE	380.12	0.00	0.00	0.00

Dual graph

Density: 9.90%
MCB compute time (ms): 292
MCB cycles: 1,712
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Dual1.json

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

Clustering coefficient 0.47 0.82 0.51 0.50 92.12 0.00 -121.30 0.05 0.10 4.12

Degree 8 26 17.72 18.00 3,190 MAX VALUE 514.11 3.30 0.19 2.54

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.14 3.00 5,383 MAX VALUE 1,951.24 0.37 0.12 0.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.82	0.51	0.50	92.12	0.00	-121.30	0.05	0.10	4.12
Degree	8	26	17.72	18.00	3,190	MAX VALUE	514.11	3.30	0.19	2.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.14	3.00	5,383	MAX VALUE	1,951.24	0.37	0.12	0.43

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 73
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 224.10 0.78 0.22 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.69 7.00 943 MAX VALUE 266.06 1.07 0.16 1.47

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	224.10	0.78	0.22	1.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.69	7.00	943	MAX VALUE	266.06	1.07	0.16	1.47

Triangulated dual graph

Density: 45.65%
Triangles: 188,099

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

Clustering coefficient 0.66 1.00 0.83 0.81 149.39 0.00 -34.66 0.09 0.11 4.52

Degree 8 137 81.72 97.00 14,710 MAX VALUE 757.28 39.84 0.49 4.02

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	0.66	1.00	0.83	0.81	149.39	0.00	-34.66	0.09	0.11	4.52
Degree	8	137	81.72	97.00	14,710	MAX VALUE	757.28	39.84	0.49	4.02
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.35%

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

Clustering coefficient 0.51 1.00 0.80 0.75 143.38 0.00 -44.61 0.16 0.20 3.24

Degree 2 63 20.32 7.00 3,658 MAX VALUE 418.24 22.36 1.10 3.10

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	143.38	0.00	-44.61	0.16	0.20	3.24
Degree	2	63	20.32	7.00	3,658	MAX VALUE	418.24	22.36	1.10	3.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 40
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-98-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 14 3.27 2.00 720 MAX VALUE 209.98 2.95 0.90 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.34 6.00 894 MAX VALUE 259.54 0.75 0.12 0.46

XCSP 2.1 Benchmarks