XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-5-ext
Number of variables: 15
Number of constraints: 105
Satisfiable: True
Timestamp: 2025-07-20 22:08:33
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 15
Number of constraints: 105

General features

Coarse blocks: 3,070
Value tables: 15

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

Arity 2 2 2.00 2.00 210 4.06e+31 72.78 0.00 0.00 0.00

Coarse blocks size 1 14 13.07 14.00 40,120 MAX VALUE 7,521.31 3.35 0.26 0.26

Relational linkage 0.07 0.07 0.07 0.07 9.67 0.00 -392.67 0.00 0.00 0.00

Tightness 0.07 0.96 0.15 0.07 15.84 0.00 -257.77 0.26 1.72 0.47

Tuples 9 210 191.05 210.00 20,060 MAX VALUE 531.87 58.42 0.31 0.47

Values 15 15 15.00 15.00 225 4.38e+17 40.62 0.00 0.00 0.00

Value table constraints 14 14 14.00 14.00 210 1.56e+17 39.59 0.00 0.00 0.00

Value table partitions 15 15 15.00 15.00 225 4.38e+17 40.62 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	210	4.06e+31	72.78	0.00	0.00	0.00
Coarse blocks size	1	14	13.07	14.00	40,120	MAX VALUE	7,521.31	3.35	0.26	0.26
Relational linkage	0.07	0.07	0.07	0.07	9.67	0.00	-392.67	0.00	0.00	0.00
Tightness	0.07	0.96	0.15	0.07	15.84	0.00	-257.77	0.26	1.72	0.47
Tuples	9	210	191.05	210.00	20,060	MAX VALUE	531.87	58.42	0.31	0.47
Values	15	15	15.00	15.00	225	4.38e+17	40.62	0.00	0.00	0.00
Value table constraints	14	14	14.00	14.00	210	1.56e+17	39.59	0.00	0.00	0.00
Value table partitions	15	15	15.00	15.00	225	4.38e+17	40.62	0.00	0.00	0.00

Tree decomposition

Number of clusters: 1
Number of leaves: 1
Tree depth: 0
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Tree1.json

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

Cluster constraints 105 105 105.00 105.00 105 105 4.65 0.00 0.00 0.00

Variables per cluster 15 15 15.00 15.00 15 15 2.71 0.00 0.00 0.00

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

Separator variables 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Clusters per var 1 1 1.00 1.00 15 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	105	105	105.00	105.00	105	105	4.65	0.00
Variables per cluster	15	15	15.00	15.00	15	15	2.71	0.00
Separator constraints	0	0	0.00	0.00	0	0	None	None
Separator variables	0	0	0.00	0.00	0	0	None	None
Clusters per var	1	1	1.00	1.00	15	1	0.00	0.00

Dual tree decomposition

Number of clusters: 13
Number of leaves: 7
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/DualTree1.json

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

Cluster constraints 195 636 308.00 195.00 4,004 6.11e+31 73.19 149.25 0.48 1.26

Variables per cluster 27 72 39.31 27.00 511 2.15e+20 46.82 15.64 0.40 1.26

Separator constraints 0 364 203.00 169.00 2,639 0 None 86.31 0.43 1.26

Separator variables 0 56 31.23 26.00 406 0 None 13.28 0.43 1.26

Clusters per variable 1 6 4.87 5.00 511 MAX VALUE 157.62 1.47 0.30 1.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	195	636	308.00	195.00	4,004	6.11e+31	73.19	149.25	0.48	1.26
Variables per cluster	27	72	39.31	27.00	511	2.15e+20	46.82	15.64	0.40	1.26
Separator constraints	0	364	203.00	169.00	2,639	0	None	86.31	0.43	1.26
Separator variables	0	56	31.23	26.00	406	0	None	13.28	0.43	1.26
Clusters per variable	1	6	4.87	5.00	511	MAX VALUE	157.62	1.47	0.30	1.35

Primal graph

Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 91
Triangles: 455
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Primal1.json

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

Clustering coefficient 1.00 1.00 1.00 1.00 15.00 1.00 0.00 0.00 0.00 0.00

Degree 14 14 14.00 14.00 210 1.56e+17 39.59 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 273 MAX VALUE 99.97 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	15.00	1.00	0.00	0.00	0.00	0.00
Degree	14	14	14.00	14.00	210	1.56e+17	39.59	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	273	MAX VALUE	99.97	0.00	0.00	0.00

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 91
Triangles: 455

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

Clustering coefficient 1.00 1.00 1.00 1.00 15.00 1.00 0.00 0.00 0.00 0.00

Degree 14 14 14.00 14.00 210 1.56e+17 39.59 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 273 MAX VALUE 99.97 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	15.00	1.00	0.00	0.00	0.00	0.00
Degree	14	14	14.00	14.00	210	1.56e+17	39.59	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	273	MAX VALUE	99.97	0.00	0.00	0.00

Dual graph

Density: 25.00%
MCB compute time (ms): 50
MCB cycles: 1,261
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Dual1.json

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

Clustering coefficient 0.52 0.52 0.52 0.52 54.60 0.00 -68.66 0.00 0.00 0.00

Degree 26 26 26.00 26.00 2,730 MAX VALUE 342.10 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 3,783 MAX VALUE 1,385.35 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	0.52	0.52	0.52	54.60	0.00	-68.66	0.00	0.00	0.00
Degree	26	26	26.00	26.00	2,730	MAX VALUE	342.10	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	3,783	MAX VALUE	1,385.35	0.00	0.00	0.00

Minimal dual graph

Density: 3.57%
MCB compute time (ms): 13
MCB cycles: 96

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

Clustering coefficient 0.00 0.33 0.01 0.00 0.83 0.00 None 0.05 6.07 0.15

Degree 2 6 3.71 4.00 390 MAX VALUE 135.13 0.85 0.23 1.18

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 5.62 6.00 540 MAX VALUE 164.14 1.02 0.18 1.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.83	0.00	None	0.05	6.07	0.15
Degree	2	6	3.71	4.00	390	MAX VALUE	135.13	0.85	0.23	1.18
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	5.62	6.00	540	MAX VALUE	164.14	1.02	0.18	1.42

Triangulated dual graph

Density: 75.00%
Triangles: 97,763

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

Clustering coefficient 0.85 1.00 0.89 0.87 93.43 0.00 -12.41 0.05 0.06 1.96

Degree 26 93 78.00 90.00 8,190 MAX VALUE 452.07 20.37 0.26 1.96

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	0.85	1.00	0.89	0.87	93.43	0.00	-12.41	0.05	0.06	1.96
Degree	26	93	78.00	90.00	8,190	MAX VALUE	452.07	20.37	0.26	1.96
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 15.44%

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

Clustering coefficient 0.49 1.00 0.78 0.69 82.02 0.00 -28.41 0.17 0.22 3.12

Degree 2 42 16.06 8.00 1,686 MAX VALUE 239.43 14.73 0.92 2.85

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	0.49	1.00	0.78	0.69	82.02	0.00	-28.41	0.17	0.22	3.12
Degree	2	42	16.06	8.00	1,686	MAX VALUE	239.43	14.73	0.92	2.85
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.94%
MCB compute time (ms): 5
MCB cycles: 91
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-5-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 14 3.50 2.00 420 MAX VALUE 112.37 3.97 1.13 0.38

Eccentricity None None None None None None None None None None

MCB cycle size 6 6 6.00 6.00 546 MAX VALUE 163.05 0.00 0.00 0.00

XCSP 2.1 Benchmarks