XCSP 2.1 Benchmark Database

Instance: normalized-par-32-3-ext
Number of variables: 6352
Number of constraints: 13332
Satisfiable: True
Timestamp: 2025-07-27 21:34:15
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 6352
Number of constraints: 13332

General features

Coarse blocks: 77,576
Value tables: 7,696

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

Arity 2 3 2.53 3.00 33,792 MAX VALUE 12,131.20 0.50 0.20 0.69

Coarse blocks size 1 4 2.61 3.00 202,592 MAX VALUE 66,208.20 1.08 0.41 1.38

Relational linkage 0.50 1.00 0.64 0.50 11,357.50 0.00 -8,758.55 0.21 0.33 0.84

Tightness 0.00 0.50 0.18 0.12 2,408.50 0.00 None 0.08 0.42 0.85

Tuples 1 7 5.05 7.00 67,362 MAX VALUE 20,334.90 2.03 0.40 0.87

Values 1 2 1.98 2.00 12,563 MAX VALUE 4,305.14 0.15 0.07 0.11

Value table constraints 2 85 4.74 4.00 36,480 MAX VALUE 10,684.70 5.90 1.24 1.79

Value table partitions 1 4 2.33 2.00 17,897 MAX VALUE 6,153.76 0.77 0.33 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	3	2.53	3.00	33,792	MAX VALUE	12,131.20	0.50	0.20	0.69
Coarse blocks size	1	4	2.61	3.00	202,592	MAX VALUE	66,208.20	1.08	0.41	1.38
Relational linkage	0.50	1.00	0.64	0.50	11,357.50	0.00	-8,758.55	0.21	0.33	0.84
Tightness	0.00	0.50	0.18	0.12	2,408.50	0.00	None	0.08	0.42	0.85
Tuples	1	7	5.05	7.00	67,362	MAX VALUE	20,334.90	2.03	0.40	0.87
Values	1	2	1.98	2.00	12,563	MAX VALUE	4,305.14	0.15	0.07	0.11
Value table constraints	2	85	4.74	4.00	36,480	MAX VALUE	10,684.70	5.90	1.24	1.79
Value table partitions	1	4	2.33	2.00	17,897	MAX VALUE	6,153.76	0.77	0.33	0.55

Tree decomposition

Number of clusters: 3,978
Number of leaves: 1,283
Tree depth: 33
CIR: 0.94
Independent Cluster Pairs: 7,455,710
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Tree1.json

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

Cluster constraints 1 51 7.90 8.00 31,420 MAX VALUE 7,364.34 5.94 0.75 2.60

Variables per cluster 3 102 11.09 8.00 44,101 MAX VALUE 8,558.29 11.84 1.07 2.73

Separator constraints 0 50 4.55 4.00 18,088 0 None 5.59 1.23 2.39

Separator variables 0 100 9.49 6.00 37,749 0 None 11.02 1.16 2.59

Clusters per var 1 360 6.94 3.00 44,101 MAX VALUE 7,761.55 21.83 3.14 2.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	51	7.90	8.00	31,420	MAX VALUE	7,364.34	5.94	0.75	2.60
Variables per cluster	3	102	11.09	8.00	44,101	MAX VALUE	8,558.29	11.84	1.07	2.73
Separator constraints	0	50	4.55	4.00	18,088	0	None	5.59	1.23	2.39
Separator variables	0	100	9.49	6.00	37,749	0	None	11.02	1.16	2.59
Clusters per var	1	360	6.94	3.00	44,101	MAX VALUE	7,761.55	21.83	3.14	2.49

Dual tree decomposition

Number of clusters: 5,844
Number of leaves: 3,009
Tree depth: 94
CIR: 0.99
Independent Cluster Pairs: 16,866,000
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/DualTree1.json

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

Cluster constraints 2 6,200 304.90 28.00 1,781,850 MAX VALUE 21,242.70 822.46 2.70 3.62

Variables per cluster 3 328 27.28 10.00 159,408 MAX VALUE 15,184.20 49.17 1.80 3.18

Separator constraints 0 4,928 270.79 20.00 1,582,510 0 None 742.03 2.74 3.48

Separator variables 0 256 25.00 8.00 146,076 0 None 46.24 1.85 2.81

Clusters per variable 1 76 11.96 6.00 159,408 MAX VALUE 24,038.50 13.14 1.10 3.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	6,200	304.90	28.00	1,781,850	MAX VALUE	21,242.70	822.46	2.70	3.62
Variables per cluster	3	328	27.28	10.00	159,408	MAX VALUE	15,184.20	49.17	1.80	3.18
Separator constraints	0	4,928	270.79	20.00	1,582,510	0	None	742.03	2.74	3.48
Separator variables	0	256	25.00	8.00	146,076	0	None	46.24	1.85	2.81
Clusters per variable	1	76	11.96	6.00	159,408	MAX VALUE	24,038.50	13.14	1.10	3.21

Primal graph

Density: 0.13%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.47 0.56 2,987.21 0.00 None 0.24 0.51 1.97

Degree 2 169 8.26 6.00 52,488 MAX VALUE 12,079.40 12.78 1.55 1.83

Eccentricity 22 42 32.86 34.00 208,702 MAX VALUE 22,068.60 6.02 0.18 3.03

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	0.47	0.56	2,987.21	0.00	None	0.24	0.51	1.97
Degree	2	169	8.26	6.00	52,488	MAX VALUE	12,079.40	12.78	1.55	1.83
Eccentricity	22	42	32.86	34.00	208,702	MAX VALUE	22,068.60	6.02	0.18	3.03
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 0.49%
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 0.08 1.00 0.78 0.77 4,952.22 0.00 -1,779.37 0.17 0.22 4.53

Degree 2 843 31.25 11.00 198,490 MAX VALUE 16,898.90 69.80 2.23 3.72

Eccentricity 9 18 14.16 14.00 89,968 MAX VALUE 16,830.00 0.67 0.05 0.96

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	0.08	1.00	0.78	0.77	4,952.22	0.00	-1,779.37	0.17	0.22	4.53
Degree	2	843	31.25	11.00	198,490	MAX VALUE	16,898.90	69.80	2.23	3.72
Eccentricity	9	18	14.16	14.00	89,968	MAX VALUE	16,830.00	0.67	0.05	0.96
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: None%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Dual1.json

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

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	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
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.03%
MCB compute time (ms): None
MCB cycles: None

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

Clustering coefficient 0.00 0.33 0.02 0.00 241.37 0.00 None 0.05 2.67 0.50

Degree 2 6 3.91 4.00 52,192 MAX VALUE 17,895.70 0.79 0.20 1.16

Eccentricity 32 63 47.82 48.00 637,570 MAX VALUE 51,366.90 8.01 0.17 3.36

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	0.33	0.02	0.00	241.37	0.00	None	0.05	2.67	0.50
Degree	2	6	3.91	4.00	52,192	MAX VALUE	17,895.70	0.79	0.20	1.16
Eccentricity	32	63	47.82	48.00	637,570	MAX VALUE	51,366.90	8.01	0.17	3.36
MCB cycle size	None	None	None	None	None	None	None	None	None	None

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: 0.89%

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

Clustering coefficient 0.29 1.00 0.78 0.76 10,401.00 0.00 -3,653.63 0.17 0.22 5.14

Degree 2 1,450 118.39 9.00 1,578,420 MAX VALUE 37,858.30 247.55 2.09 4.30

Eccentricity 14 27 20.87 21.00 278,207 MAX VALUE 40,487.90 1.06 0.05 1.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.29	1.00	0.78	0.76	10,401.00	0.00	-3,653.63	0.17	0.22	5.14
Degree	2	1,450	118.39	9.00	1,578,420	MAX VALUE	37,858.30	247.55	2.09	4.30
Eccentricity	14	27	20.87	21.00	278,207	MAX VALUE	40,487.90	1.06	0.05	1.45

Incidence graph

Density: 0.02%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-3-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 85 3.43 3.00 67,584 MAX VALUE 21,884.30 3.85 1.12 1.45

Eccentricity 44 86 67.15 70.00 1,321,780 MAX VALUE 82,475.20 11.96 0.18 3.65

MCB cycle size None None None None None None None None None None

XCSP 2.1 Benchmarks