XCSP 2.1 Benchmark Database

Instance: normalized-par-32-5-ext
Number of variables: 6352
Number of constraints: 13360
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: 13360

General features

Coarse blocks: 77,803
Value tables: 7,696

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

Arity 2 3 2.54 3.00 33,904 MAX VALUE 12,173.30 0.50 0.20 0.69

Coarse blocks size 1 4 2.62 3.00 203,648 MAX VALUE 66,604.50 1.08 0.41 1.38

Relational linkage 0.50 1.00 0.64 0.50 11,369.50 0.00 -8,739.08 0.21 0.33 0.85

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

Tuples 1 7 5.07 7.00 67,685 MAX VALUE 20,415.30 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 4.75 4.00 36,592 MAX VALUE 10,697.50 5.97 1.26 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	2.54	3.00	33,904	MAX VALUE	12,173.30	0.50	0.20	0.69
Coarse blocks size	1	4	2.62	3.00	203,648	MAX VALUE	66,604.50	1.08	0.41	1.38
Relational linkage	0.50	1.00	0.64	0.50	11,369.50	0.00	-8,739.08	0.21	0.33	0.85
Tightness	0.00	0.50	0.18	0.12	2,408.50	0.00	None	0.08	0.42	0.85
Tuples	1	7	5.07	7.00	67,685	MAX VALUE	20,415.30	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	4.75	4.00	36,592	MAX VALUE	10,697.50	5.97	1.26	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: 3,957
Number of leaves: 1,248
Tree depth: 30
CIR: 0.95
Independent Cluster Pairs: 7,401,940
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Tree1.json

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

Cluster constraints 0 50 7.87 8.00 31,127 None None 5.77 0.73 2.59

Variables per cluster 3 100 10.98 8.00 43,441 MAX VALUE 8,500.82 11.46 1.04 2.73

Separator constraints 0 49 4.49 4.00 17,767 0 None 5.38 1.20 2.38

Separator variables 0 98 9.37 6.00 37,089 0 None 10.61 1.13 2.59

Clusters per var 1 299 6.84 3.00 43,441 MAX VALUE 7,779.14 20.83 3.05 2.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	50	7.87	8.00	31,127	None	None	5.77	0.73	2.59
Variables per cluster	3	100	10.98	8.00	43,441	MAX VALUE	8,500.82	11.46	1.04	2.73
Separator constraints	0	49	4.49	4.00	17,767	0	None	5.38	1.20	2.38
Separator variables	0	98	9.37	6.00	37,089	0	None	10.61	1.13	2.59
Clusters per var	1	299	6.84	3.00	43,441	MAX VALUE	7,779.14	20.83	3.05	2.49

Dual tree decomposition

Number of clusters: 5,846
Number of leaves: 2,999
Tree depth: 104
CIR: 0.99
Independent Cluster Pairs: 16,873,400
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/DualTree1.json

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

Cluster constraints 2 6,668 323.95 28.00 1,893,840 MAX VALUE 21,355.50 882.17 2.72 3.64

Variables per cluster 3 332 27.95 10.00 163,368 MAX VALUE 15,241.20 50.57 1.81 3.18

Separator constraints 0 5,936 289.19 20.00 1,690,630 0 None 801.97 2.77 3.50

Separator variables 0 256 25.66 8.00 150,008 0 None 47.72 1.86 2.81

Clusters per variable 1 86 12.23 6.00 163,368 MAX VALUE 24,226.80 13.66 1.12 3.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	6,668	323.95	28.00	1,893,840	MAX VALUE	21,355.50	882.17	2.72	3.64
Variables per cluster	3	332	27.95	10.00	163,368	MAX VALUE	15,241.20	50.57	1.81	3.18
Separator constraints	0	5,936	289.19	20.00	1,690,630	0	None	801.97	2.77	3.50
Separator variables	0	256	25.66	8.00	150,008	0	None	47.72	1.86	2.81
Clusters per variable	1	86	12.23	6.00	163,368	MAX VALUE	24,226.80	13.66	1.12	3.23

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-32-5-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-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 2,980.51 0.00 None 0.24 0.51 1.97

Degree 2 169 8.31 6.00 52,768 MAX VALUE 12,102.20 12.95 1.56 1.83

Eccentricity 22 42 32.86 34.00 208,702 MAX VALUE 22,068.50 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	2,980.51	0.00	None	0.24	0.51	1.97
Degree	2	169	8.31	6.00	52,768	MAX VALUE	12,102.20	12.95	1.56	1.83
Eccentricity	22	42	32.86	34.00	208,702	MAX VALUE	22,068.50	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 0.09 1.00 0.78 0.77 4,939.93 0.00 -1,796.57 0.17 0.22 4.54

Degree 2 709 31.03 11.00 197,078 MAX VALUE 16,915.00 67.33 2.17 3.71

Eccentricity 7 14 9.21 9.00 58,516 MAX VALUE 14,088.10 0.68 0.07 0.97

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	0.09	1.00	0.78	0.77	4,939.93	0.00	-1,796.57	0.17	0.22	4.54
Degree	2	709	31.03	11.00	197,078	MAX VALUE	16,915.00	67.33	2.17	3.71
Eccentricity	7	14	9.21	9.00	58,516	MAX VALUE	14,088.10	0.68	0.07	0.97
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-32-5-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-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 0.00 248.20 0.00 None 0.05 2.62 0.51

Degree 2 6 3.92 4.00 52,416 MAX VALUE 17,959.80 0.79 0.20 1.17

Eccentricity 32 63 48.12 49.00 642,896 MAX VALUE 51,554.30 8.13 0.17 3.37

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	248.20	0.00	None	0.05	2.62	0.51
Degree	2	6	3.92	4.00	52,416	MAX VALUE	17,959.80	0.79	0.20	1.17
Eccentricity	32	63	48.12	49.00	642,896	MAX VALUE	51,554.30	8.13	0.17	3.37
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: 0.90%

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

Clustering coefficient 0.30 1.00 0.78 0.76 10,416.10 0.00 -3,670.13 0.17 0.22 5.14

Degree 2 1,355 120.55 9.00 1,610,510 MAX VALUE 38,086.90 251.50 2.09 4.32

Eccentricity 11 21 14.15 14.00 189,080 MAX VALUE 35,361.80 1.11 0.08 1.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.30	1.00	0.78	0.76	10,416.10	0.00	-3,670.13	0.17	0.22	5.14
Degree	2	1,355	120.55	9.00	1,610,510	MAX VALUE	38,086.90	251.50	2.09	4.32
Eccentricity	11	21	14.15	14.00	189,080	MAX VALUE	35,361.80	1.11	0.08	1.50

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-32-5-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-32-5-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 85 3.44 3.00 67,808 MAX VALUE 21,939.20 3.90 1.13 1.45

Eccentricity 44 86 67.11 70.00 1,322,860 MAX VALUE 82,579.10 11.98 0.18 3.65

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

XCSP 2.1 Benchmarks