XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-2-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:24
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 21 12.55 13.00 112,990 MAX VALUE 22,581.90 2.49 0.20 2.33

Relational linkage 0.16 0.56 0.36 0.36 357.72 0.00 -1,043.84 0.06 0.17 1.85

Tightness 0.45 0.56 0.50 0.50 89.61 0.00 -125.72 0.02 0.04 3.84

Tuples 277 345 313.86 314.00 56,495 MAX VALUE 1,034.64 13.61 0.04 3.84

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

Value table constraints 3 16 9.00 9.00 360 2.98e+37 86.29 2.36 0.26 2.12

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	21	12.55	13.00	112,990	MAX VALUE	22,581.90	2.49	0.20	2.33
Relational linkage	0.16	0.56	0.36	0.36	357.72	0.00	-1,043.84	0.06	0.17	1.85
Tightness	0.45	0.56	0.50	0.50	89.61	0.00	-125.72	0.02	0.04	3.84
Tuples	277	345	313.86	314.00	56,495	MAX VALUE	1,034.64	13.61	0.04	3.84
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	16	9.00	9.00	360	2.98e+37	86.29	2.36	0.26	2.12
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: 10
Tree depth: 4
CIR: 0.06
Independent Cluster Pairs: 11
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Tree1.json

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

Cluster constraints 3 58 23.05 18.00 461 1.69e+25 58.09 14.63 0.63 2.86

Variables per cluster 4 21 11.50 10.00 230 2.40e+20 46.93 4.88 0.42 2.44

Separator constraints 0 41 14.05 8.50 281 0 None 12.79 0.91 2.79

Separator variables 0 18 9.50 8.50 190 0 None 4.88 0.51 2.44

Clusters per var 1 14 5.75 7.00 230 1.92e+24 55.91 3.88 0.67 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	58	23.05	18.00	461	1.69e+25	58.09	14.63	0.63	2.86
Variables per cluster	4	21	11.50	10.00	230	2.40e+20	46.93	4.88	0.42	2.44
Separator constraints	0	41	14.05	8.50	281	0	None	12.79	0.91	2.79
Separator variables	0	18	9.50	8.50	190	0	None	4.88	0.51	2.44
Clusters per var	1	14	5.75	7.00	230	1.92e+24	55.91	3.88	0.67	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 147
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/DualTree1.json

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

Cluster constraints 22 278 118.87 101.50 4,517 MAX VALUE 174.92 68.94 0.58 3.43

Variables per cluster 9 73 28.16 21.50 1,070 MAX VALUE 121.06 16.85 0.60 3.24

Separator constraints 0 163 78.05 66.00 2,966 0 None 41.60 0.53 3.38

Separator variables 0 56 23.42 19.50 890 0 None 12.79 0.55 3.19

Clusters per variable 1 10 5.94 6.00 1,070 MAX VALUE 291.29 2.68 0.45 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	22	278	118.87	101.50	4,517	MAX VALUE	174.92	68.94	0.58	3.43
Variables per cluster	9	73	28.16	21.50	1,070	MAX VALUE	121.06	16.85	0.60	3.24
Separator constraints	0	163	78.05	66.00	2,966	0	None	41.60	0.53	3.38
Separator variables	0	56	23.42	19.50	890	0	None	12.79	0.55	3.19
Clusters per variable	1	10	5.94	6.00	1,070	MAX VALUE	291.29	2.68	0.45	2.24

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 180
Triangles: 126
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.25 0.25 9.83 0.00 None 0.09 0.35 3.16

Degree 3 16 9.00 9.00 360 2.98e+37 86.29 2.36 0.26 2.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.40 3.00 612 MAX VALUE 218.46 0.49 0.14 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.25	0.25	9.83	0.00	None	0.09	0.35	3.16
Degree	3	16	9.00	9.00	360	2.98e+37	86.29	2.36	0.26	2.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.40	3.00	612	MAX VALUE	218.46	0.49	0.14	0.67

Triangulated primal graph

Density: 51.28%
MCB compute time (ms): 9
MCB cycles: 367
Triangles: 2,376

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

Clustering coefficient 0.62 1.00 0.84 0.83 33.45 0.00 -7.53 0.12 0.14 3.08

Degree 3 33 20.00 25.50 800 MAX VALUE 112.95 9.48 0.47 2.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,101 MAX VALUE 403.19 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.84	0.83	33.45	0.00	-7.53	0.12	0.14	3.08
Degree	3	33	20.00	25.50	800	MAX VALUE	112.95	9.48	0.47	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,101	MAX VALUE	403.19	0.00	0.00	0.00

Dual graph

Density: 9.63%
MCB compute time (ms): 187
MCB cycles: 1,985
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Dual1.json

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

Clustering coefficient 0.45 0.67 0.50 0.49 90.69 0.00 -123.81 0.04 0.07 4.01

Degree 8 27 17.23 17.00 3,102 MAX VALUE 509.30 3.18 0.18 2.51

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.31 3.00 6,574 MAX VALUE 2,354.11 0.54 0.16 0.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.67	0.50	0.49	90.69	0.00	-123.81	0.04	0.07	4.01
Degree	8	27	17.23	17.00	3,102	MAX VALUE	509.30	3.18	0.18	2.51
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.31	3.00	6,574	MAX VALUE	2,354.11	0.54	0.16	0.70

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 79
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 223.87 0.79 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.74 7.00 950 MAX VALUE 266.63 1.18 0.18 1.56

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	223.87	0.79	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.74	7.00	950	MAX VALUE	266.63	1.18	0.18	1.56

Triangulated dual graph

Density: 42.47%
Triangles: 159,910

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

Clustering coefficient 0.66 1.00 0.82 0.81 147.56 0.00 -37.13 0.10 0.12 4.57

Degree 8 129 76.02 79.00 13,684 MAX VALUE 744.95 37.92 0.50 4.01

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	0.82	0.81	147.56	0.00	-37.13	0.10	0.12	4.57
Degree	8	129	76.02	79.00	13,684	MAX VALUE	744.95	37.92	0.50	4.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.52%

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

Clustering coefficient 0.53 1.00 0.80 0.74 143.14 0.00 -44.66 0.16 0.20 3.32

Degree 2 69 20.62 7.00 3,712 MAX VALUE 417.65 22.78 1.10 3.09

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	0.80	0.74	143.14	0.00	-44.66	0.16	0.20	3.32
Degree	2	69	20.62	7.00	3,712	MAX VALUE	417.65	22.78	1.10	3.09
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 45
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-2-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 16 3.27 2.00 720 MAX VALUE 211.05 2.88 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.47 6.00 912 MAX VALUE 262.13 0.85 0.13 0.54

XCSP 2.1 Benchmarks