XCSP 2.1 Benchmark Database

Instance: normalized-par-16-1-ext
Number of variables: 2030
Number of constraints: 4249
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: 4249

General features

Coarse blocks: 19,066
Value tables: 2,606

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

Arity 2 3 2.53 3.00 10,742 MAX VALUE 3,855.05 0.50 0.20 0.69

Coarse blocks size 1 4 2.12 2.00 40,426 MAX VALUE 11,361.30 1.16 0.55 1.31

Relational linkage 0.50 1.00 0.71 0.50 3,028.75 0.00 -1,677.56 0.24 0.33 0.90

Tightness 0.00 0.25 0.11 0.12 470.00 0.00 None 0.11 0.96 1.08

Tuples 1 7 3.29 3.00 13,989 MAX VALUE 3,800.33 2.41 0.73 1.21

Values 1 2 1.60 2.00 3,244 MAX VALUE 841.48 0.49 0.31 0.67

Value table constraints 2 41 4.56 4.00 11,894 MAX VALUE 3,584.83 3.47 0.76 1.83

Value table partitions 1 4 1.66 2.00 4,313 MAX VALUE 1,077.15 0.76 0.46 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	3	2.53	3.00	10,742	MAX VALUE	3,855.05	0.50	0.20	0.69
Coarse blocks size	1	4	2.12	2.00	40,426	MAX VALUE	11,361.30	1.16	0.55	1.31
Relational linkage	0.50	1.00	0.71	0.50	3,028.75	0.00	-1,677.56	0.24	0.33	0.90
Tightness	0.00	0.25	0.11	0.12	470.00	0.00	None	0.11	0.96	1.08
Tuples	1	7	3.29	3.00	13,989	MAX VALUE	3,800.33	2.41	0.73	1.21
Values	1	2	1.60	2.00	3,244	MAX VALUE	841.48	0.49	0.31	0.67
Value table constraints	2	41	4.56	4.00	11,894	MAX VALUE	3,584.83	3.47	0.76	1.83
Value table partitions	1	4	1.66	2.00	4,313	MAX VALUE	1,077.15	0.76	0.46	0.88

Tree decomposition

Number of clusters: 1,267
Number of leaves: 388
Tree depth: 31
CIR: 0.93
Independent Cluster Pairs: 741,195
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Tree1.json

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

Cluster constraints 1 34 7.66 8.00 9,699 MAX VALUE 2,310.74 5.00 0.65 2.59

Variables per cluster 3 71 10.57 8.00 13,393 MAX VALUE 2,685.89 9.62 0.91 2.81

Separator constraints 0 30 4.30 4.00 5,450 0 None 4.33 1.01 2.37

Separator variables 0 65 8.97 6.00 11,363 0 None 8.58 0.96 2.67

Clusters per var 1 160 6.60 3.00 13,393 MAX VALUE 2,619.47 13.13 1.99 2.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	34	7.66	8.00	9,699	MAX VALUE	2,310.74	5.00	0.65	2.59
Variables per cluster	3	71	10.57	8.00	13,393	MAX VALUE	2,685.89	9.62	0.91	2.81
Separator constraints	0	30	4.30	4.00	5,450	0	None	4.33	1.01	2.37
Separator variables	0	65	8.97	6.00	11,363	0	None	8.58	0.96	2.67
Clusters per var	1	160	6.60	3.00	13,393	MAX VALUE	2,619.47	13.13	1.99	2.57

Dual tree decomposition

Number of clusters: 1,899
Number of leaves: 913
Tree depth: 38
CIR: 0.98
Independent Cluster Pairs: 1,763,440
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/DualTree1.json

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

Cluster constraints 2 1,776 93.62 28.00 177,779 MAX VALUE 6,647.95 204.01 2.18 3.66

Variables per cluster 3 162 19.35 11.00 36,745 MAX VALUE 4,833.25 24.45 1.26 3.29

Separator constraints 0 1,616 74.80 20.00 142,047 0 None 173.71 2.32 3.49

Separator variables 0 128 17.11 10.00 32,496 0 None 21.82 1.28 2.96

Clusters per variable 1 47 8.65 6.00 36,745 MAX VALUE 7,015.31 8.08 0.93 2.96

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	1,776	93.62	28.00	177,779	MAX VALUE	6,647.95	204.01	2.18	3.66
Variables per cluster	3	162	19.35	11.00	36,745	MAX VALUE	4,833.25	24.45	1.26	3.29
Separator constraints	0	1,616	74.80	20.00	142,047	0	None	173.71	2.32	3.49
Separator variables	0	128	17.11	10.00	32,496	0	None	21.82	1.28	2.96
Clusters per variable	1	47	8.65	6.00	36,745	MAX VALUE	7,015.31	8.08	0.93	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-16-1-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.45 0.49 914.79 0.00 None 0.24 0.53 2.17

Degree 2 81 8.04 8.00 16,322 MAX VALUE 3,908.35 7.31 0.91 2.01

Eccentricity 13 26 19.88 20.00 40,348 MAX VALUE 6,039.63 3.29 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	0.45	0.49	914.79	0.00	None	0.24	0.53	2.17
Degree	2	81	8.04	8.00	16,322	MAX VALUE	3,908.35	7.31	0.91	2.01
Eccentricity	13	26	19.88	20.00	40,348	MAX VALUE	6,039.63	3.29	0.17	2.49
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 1.49%
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 0.13 1.00 0.77 0.75 1,562.90 0.00 -596.63 0.18 0.23 4.60

Degree 2 451 30.32 11.00 61,552 MAX VALUE 5,476.45 52.53 1.73 3.79

Eccentricity 8 15 10.12 10.00 20,550 MAX VALUE 4,692.56 0.84 0.08 1.11

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	0.13	1.00	0.77	0.75	1,562.90	0.00	-596.63	0.18	0.23	4.60
Degree	2	451	30.32	11.00	61,552	MAX VALUE	5,476.45	52.53	1.73	3.79
Eccentricity	8	15	10.12	10.00	20,550	MAX VALUE	4,692.56	0.84	0.08	1.11
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.40%
MCB compute time (ms): 273,564
MCB cycles: 46,274
Triangles: 193,350
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.52 0.47 2,208.55 0.00 None 0.14 0.27 3.56

Degree 2 80 16.82 12.00 71,464 MAX VALUE 10,848.50 12.71 0.76 3.15

Eccentricity 14 27 20.53 21.00 87,221 MAX VALUE 12,784.40 3.22 0.16 2.48

MCB cycle size 3 18 3.36 3.00 155,363 MAX VALUE 55,174.50 0.74 0.22 0.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.52	0.47	2,208.55	0.00	None	0.14	0.27	3.56
Degree	2	80	16.82	12.00	71,464	MAX VALUE	10,848.50	12.71	0.76	3.15
Eccentricity	14	27	20.53	21.00	87,221	MAX VALUE	12,784.40	3.22	0.16	2.48
MCB cycle size	3	18	3.36	3.00	155,363	MAX VALUE	55,174.50	0.74	0.22	0.72

Minimal dual graph

Density: 0.09%
MCB compute time (ms): 657,903
MCB cycles: 3,888

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

Clustering coefficient 0.00 0.33 0.01 0.00 62.37 0.00 None 0.04 3.06 0.42

Degree 2 6 3.83 4.00 16,272 MAX VALUE 5,616.48 0.74 0.19 1.12

Eccentricity 22 40 30.88 31.00 131,188 MAX VALUE 14,523.10 4.71 0.15 2.86

MCB cycle size 3 24 5.74 5.00 22,325 MAX VALUE 6,636.43 1.80 0.31 1.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	62.37	0.00	None	0.04	3.06	0.42
Degree	2	6	3.83	4.00	16,272	MAX VALUE	5,616.48	0.74	0.19	1.12
Eccentricity	22	40	30.88	31.00	131,188	MAX VALUE	14,523.10	4.71	0.15	2.86
MCB cycle size	3	24	5.74	5.00	22,325	MAX VALUE	6,636.43	1.80	0.31	1.77

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: 1.29%

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

Clustering coefficient 0.35 1.00 0.77 0.72 3,267.49 0.00 -1,238.28 0.18 0.23 4.67

Degree 2 583 55.00 8.00 233,700 MAX VALUE 11,156.90 101.60 1.85 3.97

Eccentricity 11 22 14.78 15.00 62,807 MAX VALUE 11,433.80 1.06 0.07 1.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.35	1.00	0.77	0.72	3,267.49	0.00	-1,238.28	0.18	0.23	4.67
Degree	2	583	55.00	8.00	233,700	MAX VALUE	11,156.90	101.60	1.85	3.97
Eccentricity	11	22	14.78	15.00	62,807	MAX VALUE	11,433.80	1.06	0.07	1.38

Incidence graph

Density: 0.05%
MCB compute time (ms): 408,745
MCB cycles: 4,464
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-parExtConvert/normalized-par-16-1-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 41 3.42 3.00 21,484 MAX VALUE 7,040.62 2.46 0.72 1.47

Eccentricity 27 54 40.96 42.00 257,168 MAX VALUE 23,228.20 6.48 0.16 3.11

MCB cycle size 4 36 6.38 6.00 28,498 MAX VALUE 8,111.00 2.20 0.34 0.99

XCSP 2.1 Benchmarks