XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-5-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
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 4 22 12.58 13.00 113,206 MAX VALUE 22,600.40 2.49 0.20 2.33

Relational linkage 0.16 0.56 0.36 0.36 359.96 0.00 -1,037.61 0.06 0.17 1.85

Tightness 0.45 0.55 0.50 0.50 89.44 0.00 -126.03 0.02 0.04 3.71

Tuples 280 345 314.46 315.00 56,603 MAX VALUE 1,035.03 11.91 0.04 3.71

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

Value table constraints 5 15 9.00 8.50 360 4.22e+37 86.63 2.29 0.25 2.14

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	4	22	12.58	13.00	113,206	MAX VALUE	22,600.40	2.49	0.20	2.33
Relational linkage	0.16	0.56	0.36	0.36	359.96	0.00	-1,037.61	0.06	0.17	1.85
Tightness	0.45	0.55	0.50	0.50	89.44	0.00	-126.03	0.02	0.04	3.71
Tuples	280	345	314.46	315.00	56,603	MAX VALUE	1,035.03	11.91	0.04	3.71
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	15	9.00	8.50	360	4.22e+37	86.63	2.29	0.25	2.14
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: 9
Tree depth: 5
CIR: 0.08
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Tree1.json

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

Cluster constraints 9 56 24.60 18.50 492 1.11e+26 59.97 15.96 0.65 2.65

Variables per cluster 6 21 12.35 10.50 247 1.27e+21 48.60 5.07 0.41 2.46

Separator constraints 0 45 15.60 8.50 312 0 None 15.15 0.97 2.44

Separator variables 0 19 10.35 8.50 207 0 None 5.24 0.51 2.46

Clusters per var 1 14 6.17 6.00 247 3.39e+25 58.78 4.15 0.67 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	56	24.60	18.50	492	1.11e+26	59.97	15.96	0.65	2.65
Variables per cluster	6	21	12.35	10.50	247	1.27e+21	48.60	5.07	0.41	2.46
Separator constraints	0	45	15.60	8.50	312	0	None	15.15	0.97	2.44
Separator variables	0	19	10.35	8.50	207	0	None	5.24	0.51	2.46
Clusters per var	1	14	6.17	6.00	247	3.39e+25	58.78	4.15	0.67	2.25

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 133
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/DualTree1.json

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

Cluster constraints 37 401 125.74 95.50 4,778 MAX VALUE 175.40 90.03 0.72 3.56

Variables per cluster 12 86 29.34 22.50 1,115 MAX VALUE 122.00 19.11 0.65 3.16

Separator constraints 0 213 85.08 70.00 3,233 0 None 53.89 0.63 3.56

Separator variables 0 65 24.61 20.50 935 0 None 14.48 0.59 3.11

Clusters per variable 1 10 6.19 7.00 1,115 MAX VALUE 299.89 2.62 0.42 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	37	401	125.74	95.50	4,778	MAX VALUE	175.40	90.03	0.72	3.56
Variables per cluster	12	86	29.34	22.50	1,115	MAX VALUE	122.00	19.11	0.65	3.16
Separator constraints	0	213	85.08	70.00	3,233	0	None	53.89	0.63	3.56
Separator variables	0	65	24.61	20.50	935	0	None	14.48	0.59	3.11
Clusters per variable	1	10	6.19	7.00	1,115	MAX VALUE	299.89	2.62	0.42	2.11

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 216
Triangles: 116
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Primal1.json

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

Clustering coefficient 0.09 0.50 0.23 0.23 9.40 0.00 -59.79 0.07 0.31 3.07

Degree 5 15 9.00 8.50 360 4.22e+37 86.63 2.29 0.25 2.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.50 4.00 757 MAX VALUE 268.66 0.50 0.14 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.09	0.50	0.23	0.23	9.40	0.00	-59.79	0.07	0.31	3.07
Degree	5	15	9.00	8.50	360	4.22e+37	86.63	2.29	0.25	2.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.50	4.00	757	MAX VALUE	268.66	0.50	0.14	0.69

Triangulated primal graph

Density: 53.46%
MCB compute time (ms): 9
MCB cycles: 435
Triangles: 2,572

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

Clustering coefficient 0.65 1.00 0.84 0.81 33.57 0.00 -7.36 0.11 0.13 3.09

Degree 5 33 20.85 25.00 834 MAX VALUE 115.47 9.44 0.45 2.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,305 MAX VALUE 477.90 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.84	0.81	33.57	0.00	-7.36	0.11	0.13	3.09
Degree	5	33	20.85	25.00	834	MAX VALUE	115.47	9.44	0.45	2.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,305	MAX VALUE	477.90	0.00	0.00	0.00

Dual graph

Density: 9.59%
MCB compute time (ms): 429
MCB cycles: 1,748
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Dual1.json

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

Clustering coefficient 0.45 0.61 0.50 0.50 90.58 0.00 -123.89 0.03 0.06 4.21

Degree 11 26 17.17 17.00 3,090 MAX VALUE 508.51 3.23 0.19 2.55

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.23 3.00 5,638 MAX VALUE 2,032.62 0.44 0.14 0.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.61	0.50	0.50	90.58	0.00	-123.89	0.03	0.06	4.21
Degree	11	26	17.17	17.00	3,090	MAX VALUE	508.51	3.23	0.19	2.55
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.23	3.00	5,638	MAX VALUE	2,032.62	0.44	0.14	0.56

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 80
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.67 0.00 None 0.03 8.15 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.10 0.76 0.21 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.65 7.00 937 MAX VALUE 264.61 1.19 0.18 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.67	0.00	None	0.03	8.15	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.10	0.76	0.21	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.65	7.00	937	MAX VALUE	264.61	1.19	0.18	1.58

Triangulated dual graph

Density: 47.91%
Triangles: 210,734

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

Clustering coefficient 0.72 1.00 0.84 0.82 150.64 0.00 -32.88 0.08 0.10 4.69

Degree 11 132 85.76 104.00 15,436 MAX VALUE 765.90 41.14 0.48 3.91

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	0.72	1.00	0.84	0.82	150.64	0.00	-32.88	0.08	0.10	4.69
Degree	11	132	85.76	104.00	15,436	MAX VALUE	765.90	41.14	0.48	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.19%

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

Clustering coefficient 0.51 1.00 0.79 0.72 142.50 0.00 -45.90 0.16 0.21 3.30

Degree 2 67 20.02 7.00 3,604 MAX VALUE 415.91 21.97 1.10 3.18

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	0.79	0.72	142.50	0.00	-45.90	0.16	0.21	3.30
Degree	2	67	20.02	7.00	3,604	MAX VALUE	415.91	21.97	1.10	3.18
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-2-40-25-180-500-5-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-5-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 15 3.27 2.00 720 MAX VALUE 211.40 2.87 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.50 6.00 916 MAX VALUE 262.71 0.86 0.13 0.56

XCSP 2.1 Benchmarks