XCSP 2.1 Benchmark Database

Instance: normalized-s4-4-3-6-ext
Number of variables: 624
Number of constraints: 440
Satisfiable: True
Timestamp: 2025-07-20 22:08:50
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 624
Number of constraints: 440

General features

Coarse blocks: 3,744
Value tables: 624

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

Arity 2 26 4.25 3.00 1,872 MAX VALUE 522.97 5.27 1.24 1.19

Coarse blocks size 1 2,626 493.50 3.00 1,847,660 MAX VALUE 10,306.20 960.98 1.95 1.71

Relational linkage 0.00 0.00 0.00 0.00 0.05 0.00 -13,102.30 0.00 0.78 0.69

Tightness 0.50 1.00 0.55 0.50 243.75 0.00 -267.29 0.12 0.21 1.02

Tuples 2 2,952 164.90 4.00 72,556 MAX VALUE 740.96 669.44 4.06 1.35

Values 2 2 2.00 2.00 1,248 MAX VALUE 432.52 0.00 0.00 0.00

Value table constraints 3 3 3.00 3.00 1,872 MAX VALUE 685.53 0.00 0.00 0.00

Value table partitions 2 2 2.00 2.00 1,248 MAX VALUE 432.52 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	26	4.25	3.00	1,872	MAX VALUE	522.97	5.27	1.24	1.19
Coarse blocks size	1	2,626	493.50	3.00	1,847,660	MAX VALUE	10,306.20	960.98	1.95	1.71
Relational linkage	0.00	0.00	0.00	0.00	0.05	0.00	-13,102.30	0.00	0.78	0.69
Tightness	0.50	1.00	0.55	0.50	243.75	0.00	-267.29	0.12	0.21	1.02
Tuples	2	2,952	164.90	4.00	72,556	MAX VALUE	740.96	669.44	4.06	1.35
Values	2	2	2.00	2.00	1,248	MAX VALUE	432.52	0.00	0.00	0.00
Value table constraints	3	3	3.00	3.00	1,872	MAX VALUE	685.53	0.00	0.00	0.00
Value table partitions	2	2	2.00	2.00	1,248	MAX VALUE	432.52	0.00	0.00	0.00

Tree decomposition

Number of clusters: 226
Number of leaves: 24
Tree depth: 19
CIR: 0.58
Independent Cluster Pairs: 14,682
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Tree1.json

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

Cluster constraints 0 3 1.95 2.00 440 0 None 0.65 0.33 0.61

Variables per cluster 29 187 48.93 43.00 11,059 MAX VALUE 860.21 26.05 0.53 3.21

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 136 46.17 41.50 10,435 0 None 21.16 0.46 3.19

Clusters per var 1 45 17.72 19.00 11,059 MAX VALUE 1,605.49 10.49 0.59 3.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	3	1.95	2.00	440	0	None	0.65	0.33	0.61
Variables per cluster	29	187	48.93	43.00	11,059	MAX VALUE	860.21	26.05	0.53	3.21
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	136	46.17	41.50	10,435	0	None	21.16	0.46	3.19
Clusters per var	1	45	17.72	19.00	11,059	MAX VALUE	1,605.49	10.49	0.59	3.58

Dual tree decomposition

Number of clusters: 364
Number of leaves: 130
Tree depth: 18
CIR: 0.47
Independent Cluster Pairs: 31,174
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/DualTree1.json

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

Cluster constraints 6 14 9.07 9.00 3,302 MAX VALUE 788.96 2.46 0.27 1.75

Variables per cluster 5 27 11.64 8.50 4,238 MAX VALUE 830.63 7.25 0.62 2.01

Separator constraints 0 8 3.93 4.00 1,430 0 None 2.15 0.55 1.57

Separator variables 0 25 10.43 7.00 3,798 0 None 6.94 0.67 2.02

Clusters per variable 1 156 9.63 3.00 4,238 MAX VALUE 503.09 27.19 2.82 2.08

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	14	9.07	9.00	3,302	MAX VALUE	788.96	2.46	0.27	1.75
Variables per cluster	5	27	11.64	8.50	4,238	MAX VALUE	830.63	7.25	0.62	2.01
Separator constraints	0	8	3.93	4.00	1,430	0	None	2.15	0.55	1.57
Separator variables	0	25	10.43	7.00	3,798	0	None	6.94	0.67	2.02
Clusters per variable	1	156	9.63	3.00	4,238	MAX VALUE	503.09	27.19	2.82	2.08

Primal graph

Density: 4.71%
MCB compute time (ms): 61,016
MCB cycles: 8,529
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Primal1.json

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

Clustering coefficient 0.66 0.80 0.73 0.72 456.79 0.00 -196.21 0.05 0.07 1.33

Degree 28 31 29.33 29.50 18,304 MAX VALUE 2,107.88 1.11 0.04 1.33

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.09 3.00 26,396 MAX VALUE 9,602.80 0.29 0.09 0.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.66	0.80	0.73	0.72	456.79	0.00	-196.21	0.05	0.07	1.33
Degree	28	31	29.33	29.50	18,304	MAX VALUE	2,107.88	1.11	0.04	1.33
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.09	3.00	26,396	MAX VALUE	9,602.80	0.29	0.09	0.31

Triangulated primal graph

Density: 28.55%
MCB compute time (ms): 44,505
MCB cycles: 70,642
Triangles: None

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

Clustering coefficient 0.58 1.00 0.81 0.79 502.91 0.00 -142.14 0.12 0.15 5.70

Degree 28 356 177.84 171.00 110,972 MAX VALUE 3,052.47 111.66 0.63 5.01

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 211,926 MAX VALUE 77,608.20 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.58	1.00	0.81	0.79	502.91	0.00	-142.14	0.12	0.15	5.70
Degree	28	356	177.84	171.00	110,972	MAX VALUE	3,052.47	111.66	0.63	5.01
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	211,926	MAX VALUE	77,608.20	0.00	0.00	0.00

Dual graph

Density: 1.94%
MCB compute time (ms): 801
MCB cycles: 1,456
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Dual1.json

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

Clustering coefficient 0.02 0.33 0.21 0.20 91.59 0.00 -745.76 0.08 0.39 1.19

Degree 4 52 8.51 6.00 3,744 MAX VALUE 827.95 10.54 1.24 1.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.58 4.00 5,209 MAX VALUE 1,840.94 0.51 0.14 0.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.02	0.33	0.21	0.20	91.59	0.00	-745.76	0.08	0.39	1.19
Degree	4	52	8.51	6.00	3,744	MAX VALUE	827.95	10.54	1.24	1.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.58	4.00	5,209	MAX VALUE	1,840.94	0.51	0.14	0.72

Minimal dual graph

Density: 1.29%
MCB compute time (ms): 1,092
MCB cycles: 809

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 4 26 5.67 4.00 2,496 MAX VALUE 700.25 4.92 0.87 1.03

Eccentricity None None None None None None None None None None

MCB cycle size 4 6 4.87 4.00 3,936 MAX VALUE 1,263.42 0.99 0.20 0.68

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	4	26	5.67	4.00	2,496	MAX VALUE	700.25	4.92	0.87	1.03
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	6	4.87	4.00	3,936	MAX VALUE	1,263.42	0.99	0.20	0.68

Triangulated dual graph

Density: 5.62%
Triangles: 45,236

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

Clustering coefficient 0.13 1.00 0.84 0.86 368.90 0.00 -97.47 0.18 0.21 2.30

Degree 4 231 24.65 11.00 10,848 MAX VALUE 1,131.41 42.38 1.72 2.17

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	0.13	1.00	0.84	0.86	368.90	0.00	-97.47	0.18	0.21	2.30
Degree	4	231	24.65	11.00	10,848	MAX VALUE	1,131.41	42.38	1.72	2.17
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 4.81%

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

Clustering coefficient 0.11 1.00 0.82 0.78 360.44 0.00 -107.02 0.18 0.22 2.32

Degree 4 256 21.10 9.00 9,286 MAX VALUE 1,066.65 37.13 1.76 2.46

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	0.11	1.00	0.82	0.78	360.44	0.00	-107.02	0.18	0.22	2.32
Degree	4	256	21.10	9.00	9,286	MAX VALUE	1,066.65	37.13	1.76	2.46
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 0.33%
MCB compute time (ms): 2,007
MCB cycles: 809
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-routingExtConvert/normalized-s4-4-3-6-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 26 3.52 3.00 3,744 MAX VALUE 1,208.50 3.44 0.98 0.73

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 6,472 MAX VALUE 1,682.27 0.00 0.00 0.00

XCSP 2.1 Benchmarks