XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-44-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 12.54 13.00 112,886 MAX VALUE 22,574.00 2.49 0.20 2.33

Relational linkage 0.16 0.64 0.36 0.36 358.48 0.00 -1,041.69 0.06 0.17 1.84

Tightness 0.44 0.56 0.50 0.50 89.69 0.00 -125.54 0.02 0.04 3.71

Tuples 277 352 313.57 314.00 56,443 MAX VALUE 1,034.49 12.97 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 2 13 9.00 9.00 360 2.19e+37 85.98 2.35 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	22	12.54	13.00	112,886	MAX VALUE	22,574.00	2.49	0.20	2.33
Relational linkage	0.16	0.64	0.36	0.36	358.48	0.00	-1,041.69	0.06	0.17	1.84
Tightness	0.44	0.56	0.50	0.50	89.69	0.00	-125.54	0.02	0.04	3.71
Tuples	277	352	313.57	314.00	56,443	MAX VALUE	1,034.49	12.97	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	2	13	9.00	9.00	360	2.19e+37	85.98	2.35	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: 9
Tree depth: 4
CIR: 0.12
Independent Cluster Pairs: 21
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Tree1.json

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

Cluster constraints 2 49 22.40 20.50 448 5.59e+24 56.98 14.23 0.64 2.79

Variables per cluster 3 21 11.50 10.00 230 1.49e+20 46.45 5.31 0.46 2.55

Separator constraints 0 43 13.40 10.00 268 0 None 12.24 0.91 2.58

Separator variables 0 20 9.50 8.00 190 0 None 5.31 0.56 2.62

Clusters per var 1 14 5.75 5.50 230 1.41e+24 55.61 4.04 0.70 2.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	49	22.40	20.50	448	5.59e+24	56.98	14.23	0.64	2.79
Variables per cluster	3	21	11.50	10.00	230	1.49e+20	46.45	5.31	0.46	2.55
Separator constraints	0	43	13.40	10.00	268	0	None	12.24	0.91	2.58
Separator variables	0	20	9.50	8.00	190	0	None	5.31	0.56	2.62
Clusters per var	1	14	5.75	5.50	230	1.41e+24	55.61	4.04	0.70	2.30

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.18
Independent Cluster Pairs: 117
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/DualTree1.json

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

Cluster constraints 36 383 126.34 106.00 4,801 MAX VALUE 176.77 83.30 0.66 3.53

Variables per cluster 11 87 29.53 21.50 1,122 MAX VALUE 122.17 19.41 0.66 3.11

Separator constraints 0 215 85.55 82.00 3,251 0 None 49.00 0.57 3.49

Separator variables 0 68 24.79 19.00 942 0 None 14.87 0.60 3.08

Clusters per variable 1 11 6.23 7.00 1,122 MAX VALUE 299.71 2.72 0.44 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	36	383	126.34	106.00	4,801	MAX VALUE	176.77	83.30	0.66	3.53
Variables per cluster	11	87	29.53	21.50	1,122	MAX VALUE	122.17	19.41	0.66	3.11
Separator constraints	0	215	85.55	82.00	3,251	0	None	49.00	0.57	3.49
Separator variables	0	68	24.79	19.00	942	0	None	14.87	0.60	3.08
Clusters per variable	1	11	6.23	7.00	1,122	MAX VALUE	299.71	2.72	0.44	2.19

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 172
Triangles: 124
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Primal1.json

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

Clustering coefficient 0.00 0.48 0.24 0.24 9.64 0.00 None 0.07 0.31 3.05

Degree 2 13 9.00 9.00 360 2.19e+37 85.98 2.35 0.26 2.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 578 MAX VALUE 206.80 0.48 0.14 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.48	0.24	0.24	9.64	0.00	None	0.07	0.31	3.05
Degree	2	13	9.00	9.00	360	2.19e+37	85.98	2.35	0.26	2.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	578	MAX VALUE	206.80	0.48	0.14	0.65

Triangulated primal graph

Density: 51.28%
MCB compute time (ms): 11
MCB cycles: 384
Triangles: 2,419

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

Clustering coefficient 0.62 1.00 0.84 0.83 33.61 0.00 -7.31 0.11 0.13 3.19

Degree 2 33 20.00 24.50 800 MAX VALUE 112.20 9.70 0.49 2.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,152 MAX VALUE 421.87 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	33.61	0.00	-7.31	0.11	0.13	3.19
Degree	2	33	20.00	24.50	800	MAX VALUE	112.20	9.70	0.49	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,152	MAX VALUE	421.87	0.00	0.00	0.00

Dual graph

Density: 9.62%
MCB compute time (ms): 414
MCB cycles: 1,505
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Dual1.json

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

Clustering coefficient 0.47 0.83 0.50 0.49 90.64 0.00 -124.00 0.04 0.08 3.95

Degree 10 24 17.22 17.00 3,100 MAX VALUE 509.88 2.76 0.16 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.11 3.00 4,678 MAX VALUE 1,700.24 0.31 0.10 0.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.83	0.50	0.49	90.64	0.00	-124.00	0.04	0.08	3.95
Degree	10	24	17.22	17.00	3,100	MAX VALUE	509.88	2.76	0.16	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.11	3.00	4,678	MAX VALUE	1,700.24	0.31	0.10	0.35

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 69
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 224.25 0.77 0.22 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 4 8 6.62 7.00 933 MAX VALUE 264.51 1.04 0.16 1.40

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	224.25	0.77	0.22	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	8	6.62	7.00	933	MAX VALUE	264.51	1.04	0.16	1.40

Triangulated dual graph

Density: 48.15%
Triangles: 213,578

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

Clustering coefficient 0.71 1.00 0.84 0.83 151.31 0.00 -32.15 0.08 0.10 4.68

Degree 10 136 86.19 103.00 15,514 MAX VALUE 766.60 41.51 0.48 3.93

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	0.71	1.00	0.84	0.83	151.31	0.00	-32.15	0.08	0.10	4.68
Degree	10	136	86.19	103.00	15,514	MAX VALUE	766.60	41.51	0.48	3.93
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.23%

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

Clustering coefficient 0.51 1.00 0.79 0.72 142.31 0.00 -46.04 0.16 0.21 3.23

Degree 2 64 20.10 7.00 3,618 MAX VALUE 418.14 22.04 1.10 3.08

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	142.31	0.00	-46.04	0.16	0.21	3.23
Degree	2	64	20.10	7.00	3,618	MAX VALUE	418.14	22.04	1.10	3.08
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-2-40-25-180-500-44-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-44-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 13 3.27 2.00 720 MAX VALUE 210.75 2.88 0.88 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.44 6.00 908 MAX VALUE 261.56 0.83 0.13 0.53

XCSP 2.1 Benchmarks