XCSP 2.1 Benchmark Database

Instance: normalized-par-16-2-ext
Number of variables: 2030
Number of constraints: 4313
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: 4313

General features

Coarse blocks: 19,728
Value tables: 2,606

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

Arity 2 3 2.55 3.00 10,998 MAX VALUE 3,951.31 0.50 0.20 0.69

Coarse blocks size 1 4 2.18 2.00 43,030 MAX VALUE 12,330.80 1.17 0.54 1.32

Relational linkage 0.50 1.00 0.71 0.50 3,045.25 0.00 -1,720.11 0.23 0.33 0.92

Tightness 0.00 0.25 0.11 0.12 488.75 0.00 None 0.10 0.92 1.09

Tuples 1 7 3.44 3.00 14,843 MAX VALUE 4,061.49 2.45 0.71 1.22

Values 1 2 1.62 2.00 3,294 MAX VALUE 876.14 0.48 0.30 0.66

Value table constraints 2 43 4.66 4.00 12,150 MAX VALUE 3,622.45 3.84 0.82 1.83

Value table partitions 1 4 1.67 2.00 4,363 MAX VALUE 1,111.81 0.76 0.45 0.87

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	3	2.55	3.00	10,998	MAX VALUE	3,951.31	0.50	0.20	0.69
Coarse blocks size	1	4	2.18	2.00	43,030	MAX VALUE	12,330.80	1.17	0.54	1.32
Relational linkage	0.50	1.00	0.71	0.50	3,045.25	0.00	-1,720.11	0.23	0.33	0.92
Tightness	0.00	0.25	0.11	0.12	488.75	0.00	None	0.10	0.92	1.09
Tuples	1	7	3.44	3.00	14,843	MAX VALUE	4,061.49	2.45	0.71	1.22
Values	1	2	1.62	2.00	3,294	MAX VALUE	876.14	0.48	0.30	0.66
Value table constraints	2	43	4.66	4.00	12,150	MAX VALUE	3,622.45	3.84	0.82	1.83
Value table partitions	1	4	1.67	2.00	4,363	MAX VALUE	1,111.81	0.76	0.45	0.87

Tree decomposition

Number of clusters: 1,230
Number of leaves: 385
Tree depth: 30
CIR: 0.91
Independent Cluster Pairs: 687,667
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Tree1.json

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

Cluster constraints 1 34 8.04 8.00 9,889 MAX VALUE 2,334.44 4.89 0.61 2.59

Variables per cluster 3 68 11.06 8.50 13,610 MAX VALUE 2,683.00 9.68 0.87 2.82

Separator constraints 0 27 4.53 4.00 5,576 0 None 4.32 0.95 2.38

Separator variables 0 59 9.41 7.00 11,580 0 None 8.62 0.92 2.69

Clusters per var 1 176 6.70 3.00 13,610 MAX VALUE 2,604.01 14.24 2.12 2.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	34	8.04	8.00	9,889	MAX VALUE	2,334.44	4.89	0.61	2.59
Variables per cluster	3	68	11.06	8.50	13,610	MAX VALUE	2,683.00	9.68	0.87	2.82
Separator constraints	0	27	4.53	4.00	5,576	0	None	4.32	0.95	2.38
Separator variables	0	59	9.41	7.00	11,580	0	None	8.62	0.92	2.69
Clusters per var	1	176	6.70	3.00	13,610	MAX VALUE	2,604.01	14.24	2.12	2.56

Dual tree decomposition

Number of clusters: 1,886
Number of leaves: 938
Tree depth: 41
CIR: 0.98
Independent Cluster Pairs: 1,735,740
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/DualTree1.json

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

Cluster constraints 2 1,736 114.32 35.00 215,610 MAX VALUE 6,823.15 245.81 2.15 3.68

Variables per cluster 3 164 20.81 11.00 39,242 MAX VALUE 4,907.16 26.37 1.27 3.27

Separator constraints 0 1,656 92.97 25.00 175,340 0 None 210.41 2.26 3.53

Separator variables 0 128 18.52 10.00 34,929 0 None 23.65 1.28 2.93

Clusters per variable 1 53 9.10 6.00 39,242 MAX VALUE 7,303.82 8.40 0.92 2.98

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	1,736	114.32	35.00	215,610	MAX VALUE	6,823.15	245.81	2.15	3.68
Variables per cluster	3	164	20.81	11.00	39,242	MAX VALUE	4,907.16	26.37	1.27	3.27
Separator constraints	0	1,656	92.97	25.00	175,340	0	None	210.41	2.26	3.53
Separator variables	0	128	18.52	10.00	34,929	0	None	23.65	1.28	2.93
Clusters per variable	1	53	9.10	6.00	39,242	MAX VALUE	7,303.82	8.40	0.92	2.98

Primal graph

Density: 0.41%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.47 0.49 950.24 0.00 None 0.23 0.49 2.18

Degree 2 85 8.36 8.00 16,962 MAX VALUE 3,983.82 8.16 0.98 2.00

Eccentricity 13 25 19.81 20.00 40,222 MAX VALUE 6,032.42 3.32 0.17 2.49

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	0.49	950.24	0.00	None	0.23	0.49	2.18
Degree	2	85	8.36	8.00	16,962	MAX VALUE	3,983.82	8.16	0.98	2.00
Eccentricity	13	25	19.81	20.00	40,222	MAX VALUE	6,032.42	3.32	0.17	2.49
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 1.54%
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 0.78 0.77 1,579.60 0.00 -573.20 0.17 0.22 4.64

Degree 2 499 31.19 11.00 63,308 MAX VALUE 5,561.65 54.88 1.76 3.84

Eccentricity 5 9 6.36 6.00 12,903 MAX VALUE 3,744.01 0.65 0.10 0.95

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	0.78	0.77	1,579.60	0.00	-573.20	0.17	0.22	4.64
Degree	2	499	31.19	11.00	63,308	MAX VALUE	5,561.65	54.88	1.76	3.84
Eccentricity	5	9	6.36	6.00	12,903	MAX VALUE	3,744.01	0.65	0.10	0.95
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.43%
MCB compute time (ms): 235,499
MCB cycles: 55,601
Triangles: 259,070
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.54 0.47 2,311.01 0.00 None 0.15 0.27 3.59

Degree 2 84 18.67 14.00 80,540 MAX VALUE 11,359.30 14.56 0.78 3.19

Eccentricity 14 26 20.48 21.00 88,352 MAX VALUE 12,966.20 3.25 0.16 2.49

MCB cycle size 3 20 3.40 3.00 188,850 MAX VALUE 66,943.30 0.74 0.22 0.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.54	0.47	2,311.01	0.00	None	0.15	0.27	3.59
Degree	2	84	18.67	14.00	80,540	MAX VALUE	11,359.30	14.56	0.78	3.19
Eccentricity	14	26	20.48	21.00	88,352	MAX VALUE	12,966.20	3.25	0.16	2.49
MCB cycle size	3	20	3.40	3.00	188,850	MAX VALUE	66,943.30	0.74	0.22	0.80

Minimal dual graph

Density: 0.09%
MCB compute time (ms): 827,465
MCB cycles: 4,082

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

Clustering coefficient 0.00 0.33 0.02 0.00 73.50 0.00 None 0.05 2.79 0.47

Degree 2 6 3.89 4.00 16,784 MAX VALUE 5,774.14 0.74 0.19 1.11

Eccentricity 21 39 30.36 30.00 130,939 MAX VALUE 14,669.70 4.61 0.15 2.83

MCB cycle size 3 29 5.76 5.00 23,497 MAX VALUE 6,976.81 1.81 0.31 1.79

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.02	0.00	73.50	0.00	None	0.05	2.79	0.47
Degree	2	6	3.89	4.00	16,784	MAX VALUE	5,774.14	0.74	0.19	1.11
Eccentricity	21	39	30.36	30.00	130,939	MAX VALUE	14,669.70	4.61	0.15	2.83
MCB cycle size	3	29	5.76	5.00	23,497	MAX VALUE	6,976.81	1.81	0.31	1.79

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: 1.40%

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

Clustering coefficient 0.32 1.00 0.78 0.73 3,346.84 0.00 -1,210.64 0.18 0.23 4.70

Degree 2 566 60.17 9.00 259,500 MAX VALUE 11,588.30 109.76 1.82 4.04

Eccentricity 6 12 8.51 8.00 36,683 MAX VALUE 9,209.16 0.89 0.11 1.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.32	1.00	0.78	0.73	3,346.84	0.00	-1,210.64	0.18	0.23	4.70
Degree	2	566	60.17	9.00	259,500	MAX VALUE	11,588.30	109.76	1.82	4.04
Eccentricity	6	12	8.51	8.00	36,683	MAX VALUE	9,209.16	0.89	0.11	1.29

Incidence graph

Density: 0.05%
MCB compute time (ms): 438,630
MCB cycles: 4,656
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-2-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 43 3.47 3.00 21,996 MAX VALUE 7,174.50 2.68 0.77 1.48

Eccentricity 27 52 40.86 42.00 259,178 MAX VALUE 23,447.40 6.55 0.16 3.11

MCB cycle size 4 40 6.36 6.00 29,624 MAX VALUE 8,452.98 2.14 0.34 0.96

XCSP 2.1 Benchmarks