XCSP 2.1 Benchmark Database

Instance: normalized-par-16-3-ext
Number of variables: 2030
Number of constraints: 4283
Satisfiable: True
Timestamp: 2025-07-27 21:34:15
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 2030
Number of constraints: 4283

General features

Coarse blocks: 19,416
Value tables: 2,606

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

Arity 2 3 2.54 3.00 10,878 MAX VALUE 3,906.18 0.50 0.20 0.69

Coarse blocks size 1 4 2.15 2.00 41,806 MAX VALUE 11,875.20 1.16 0.54 1.32

Relational linkage 0.50 1.00 0.71 0.50 3,036.25 0.00 -1,701.44 0.24 0.33 0.91

Tightness 0.00 0.25 0.11 0.12 479.75 0.00 None 0.11 0.94 1.09

Tuples 1 7 3.37 3.00 14,441 MAX VALUE 3,938.14 2.44 0.72 1.22

Values 1 2 1.61 2.00 3,270 MAX VALUE 859.50 0.49 0.30 0.67

Value table constraints 2 43 4.62 4.00 12,030 MAX VALUE 3,603.86 3.67 0.79 1.83

Value table partitions 1 4 1.67 2.00 4,339 MAX VALUE 1,095.17 0.76 0.46 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	3	2.54	3.00	10,878	MAX VALUE	3,906.18	0.50	0.20	0.69
Coarse blocks size	1	4	2.15	2.00	41,806	MAX VALUE	11,875.20	1.16	0.54	1.32
Relational linkage	0.50	1.00	0.71	0.50	3,036.25	0.00	-1,701.44	0.24	0.33	0.91
Tightness	0.00	0.25	0.11	0.12	479.75	0.00	None	0.11	0.94	1.09
Tuples	1	7	3.37	3.00	14,441	MAX VALUE	3,938.14	2.44	0.72	1.22
Values	1	2	1.61	2.00	3,270	MAX VALUE	859.50	0.49	0.30	0.67
Value table constraints	2	43	4.62	4.00	12,030	MAX VALUE	3,603.86	3.67	0.79	1.83
Value table partitions	1	4	1.67	2.00	4,339	MAX VALUE	1,095.17	0.76	0.46	0.88

Tree decomposition

Number of clusters: 1,243
Number of leaves: 385
Tree depth: 27
CIR: 0.92
Independent Cluster Pairs: 711,345
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Tree1.json

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

Cluster constraints 1 33 7.82 8.00 9,721 MAX VALUE 2,312.96 4.81 0.62 2.59

Variables per cluster 3 68 10.76 8.00 13,370 MAX VALUE 2,671.06 9.46 0.88 2.82

Separator constraints 0 27 4.37 4.00 5,438 0 None 4.20 0.96 2.37

Separator variables 0 58 9.12 7.00 11,340 0 None 8.41 0.92 2.68

Clusters per var 1 155 6.59 3.00 13,370 MAX VALUE 2,612.67 13.22 2.01 2.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	33	7.82	8.00	9,721	MAX VALUE	2,312.96	4.81	0.62	2.59
Variables per cluster	3	68	10.76	8.00	13,370	MAX VALUE	2,671.06	9.46	0.88	2.82
Separator constraints	0	27	4.37	4.00	5,438	0	None	4.20	0.96	2.37
Separator variables	0	58	9.12	7.00	11,340	0	None	8.41	0.92	2.68
Clusters per var	1	155	6.59	3.00	13,370	MAX VALUE	2,612.67	13.22	2.01	2.56

Dual tree decomposition

Number of clusters: 1,888
Number of leaves: 926
Tree depth: 34
CIR: 0.98
Independent Cluster Pairs: 1,741,660
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/DualTree1.json

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

Cluster constraints 2 1,393 102.53 35.00 193,580 MAX VALUE 6,712.70 217.43 2.12 3.68

Variables per cluster 3 180 19.95 11.00 37,665 MAX VALUE 4,853.59 25.27 1.27 3.28

Separator constraints 0 1,240 82.34 22.50 155,454 0 None 183.73 2.23 3.52

Separator variables 0 136 17.68 10.00 33,382 0 None 22.48 1.27 2.95

Clusters per variable 1 41 8.79 6.00 37,665 MAX VALUE 7,149.28 8.01 0.91 2.96

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	1,393	102.53	35.00	193,580	MAX VALUE	6,712.70	217.43	2.12	3.68
Variables per cluster	3	180	19.95	11.00	37,665	MAX VALUE	4,853.59	25.27	1.27	3.28
Separator constraints	0	1,240	82.34	22.50	155,454	0	None	183.73	2.23	3.52
Separator variables	0	136	17.68	10.00	33,382	0	None	22.48	1.27	2.95
Clusters per variable	1	41	8.79	6.00	37,665	MAX VALUE	7,149.28	8.01	0.91	2.96

Primal graph

Density: 0.40%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.46 0.49 929.73 0.00 None 0.23 0.50 2.17

Degree 2 85 8.21 8.00 16,662 MAX VALUE 3,946.30 7.77 0.95 2.01

Eccentricity 14 26 20.01 20.00 40,626 MAX VALUE 6,055.67 3.19 0.16 2.47

MCB cycle size 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	0.00	1.00	0.46	0.49	929.73	0.00	None	0.23	0.50	2.17
Degree	2	85	8.21	8.00	16,662	MAX VALUE	3,946.30	7.77	0.95	2.01
Eccentricity	14	26	20.01	20.00	40,626	MAX VALUE	6,055.67	3.19	0.16	2.47
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 1.50%
MCB compute time (ms): None
MCB cycles: None
Triangles: None

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

Clustering coefficient 0.12 1.00 0.77 0.76 1,566.56 0.00 -590.95 0.17 0.23 4.65

Degree 2 460 30.38 11.00 61,672 MAX VALUE 5,516.59 51.44 1.69 3.85

Eccentricity 6 12 8.07 8.00 16,384 MAX VALUE 4,230.78 0.75 0.09 1.07

MCB cycle size 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	0.12	1.00	0.77	0.76	1,566.56	0.00	-590.95	0.17	0.23	4.65
Degree	2	460	30.38	11.00	61,672	MAX VALUE	5,516.59	51.44	1.69	3.85
Eccentricity	6	12	8.07	8.00	16,384	MAX VALUE	4,230.78	0.75	0.09	1.07
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.42%
MCB compute time (ms): 272,426
MCB cycles: 50,534
Triangles: 227,530
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.53 0.47 2,261.27 0.00 None 0.14 0.27 3.63

Degree 2 84 17.80 13.00 76,252 MAX VALUE 11,117.50 13.75 0.77 3.21

Eccentricity 14 27 20.70 21.00 88,642 MAX VALUE 12,926.00 3.12 0.15 2.47

MCB cycle size 3 18 3.37 3.00 170,145 MAX VALUE 60,410.90 0.74 0.22 0.75

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.53	0.47	2,261.27	0.00	None	0.14	0.27	3.63
Degree	2	84	17.80	13.00	76,252	MAX VALUE	11,117.50	13.75	0.77	3.21
Eccentricity	14	27	20.70	21.00	88,642	MAX VALUE	12,926.00	3.12	0.15	2.47
MCB cycle size	3	18	3.37	3.00	170,145	MAX VALUE	60,410.90	0.74	0.22	0.75

Minimal dual graph

Density: 0.09%
MCB compute time (ms): 822,089
MCB cycles: 3,990

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

Clustering coefficient 0.00 0.33 0.02 0.00 69.23 0.00 None 0.05 2.89 0.46

Degree 2 6 3.86 4.00 16,544 MAX VALUE 5,700.28 0.74 0.19 1.11

Eccentricity 22 40 30.66 31.00 131,308 MAX VALUE 14,611.50 4.57 0.15 2.83

MCB cycle size 3 25 5.76 5.00 22,985 MAX VALUE 6,823.15 1.80 0.31 1.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.02	0.00	69.23	0.00	None	0.05	2.89	0.46
Degree	2	6	3.86	4.00	16,544	MAX VALUE	5,700.28	0.74	0.19	1.11
Eccentricity	22	40	30.66	31.00	131,308	MAX VALUE	14,611.50	4.57	0.15	2.83
MCB cycle size	3	25	5.76	5.00	22,985	MAX VALUE	6,823.15	1.80	0.31	1.78

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 1.43%

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

Clustering coefficient 0.33 1.00 0.77 0.73 3,316.69 0.00 -1,211.05 0.18 0.23 4.71

Degree 2 557 61.16 8.00 261,930 MAX VALUE 11,443.20 113.69 1.86 4.00

Eccentricity 9 17 11.63 12.00 49,804 MAX VALUE 10,495.20 0.91 0.08 1.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.77	0.73	3,316.69	0.00	-1,211.05	0.18	0.23	4.71
Degree	2	557	61.16	8.00	261,930	MAX VALUE	11,443.20	113.69	1.86	4.00
Eccentricity	9	17	11.63	12.00	49,804	MAX VALUE	10,495.20	0.91	0.08	1.30

Incidence graph

Density: 0.05%
MCB compute time (ms): 500,599
MCB cycles: 4,566
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-3-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 43 3.45 3.00 21,756 MAX VALUE 7,110.79 2.58 0.75 1.48

Eccentricity 28 54 41.27 42.00 260,566 MAX VALUE 23,409.00 6.28 0.15 3.10

MCB cycle size 4 36 6.37 6.00 29,102 MAX VALUE 8,292.66 2.18 0.34 0.97

XCSP 2.1 Benchmarks