XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-25-ext
Number of variables: 75
Number of constraints: 2775
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 75
Number of constraints: 2775

General features

Coarse blocks: 414,850
Value tables: 75

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

Arity 2 2 2.00 2.00 5,550 MAX VALUE 1,923.48 0.00 0.00 0.00

Coarse blocks size 1 74 72.93 74.00 30,253,600 MAX VALUE 1,759,290.00 8.79 0.12 0.08

Relational linkage 0.01 0.01 0.01 0.01 56.33 0.00 -18,241.40 0.00 0.00 0.00

Tightness 0.01 0.99 0.03 0.01 85.79 0.00 -11,765.70 0.13 4.20 0.15

Tuples 49 5,550 5,451.10 5,550.00 15,126,800 MAX VALUE 23,698.90 730.13 0.13 0.15

Values 75 75 75.00 75.00 5,625 MAX VALUE 323.81 0.00 0.00 0.00

Value table constraints 74 74 74.00 74.00 5,550 MAX VALUE 322.81 0.00 0.00 0.00

Value table partitions 75 75 75.00 75.00 5,625 MAX VALUE 323.81 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	5,550	MAX VALUE	1,923.48	0.00	0.00	0.00
Coarse blocks size	1	74	72.93	74.00	30,253,600	MAX VALUE	1,759,290.00	8.79	0.12	0.08
Relational linkage	0.01	0.01	0.01	0.01	56.33	0.00	-18,241.40	0.00	0.00	0.00
Tightness	0.01	0.99	0.03	0.01	85.79	0.00	-11,765.70	0.13	4.20	0.15
Tuples	49	5,550	5,451.10	5,550.00	15,126,800	MAX VALUE	23,698.90	730.13	0.13	0.15
Values	75	75	75.00	75.00	5,625	MAX VALUE	323.81	0.00	0.00	0.00
Value table constraints	74	74	74.00	74.00	5,550	MAX VALUE	322.81	0.00	0.00	0.00
Value table partitions	75	75	75.00	75.00	5,625	MAX VALUE	323.81	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-3-25-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Tree1.json

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

Cluster constraints 2,775 2,775 2,775.00 2,775.00 2,775 2,775 7.93 0.00 0.00 0.00

Variables per cluster 75 75 75.00 75.00 75 75 4.32 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 75 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	2,775	2,775	2,775.00	2,775.00	2,775	2,775	7.93	0.00
Variables per cluster	75	75	75.00	75.00	75	75	4.32	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	75	1	0.00	0.00

Dual tree decomposition

Number of clusters: 73
Number of leaves: 37
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/DualTree1.json

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

Cluster constraints 5,475 86,728 14,098.00 5,475.00 1,029,150 MAX VALUE 671.28 16,032.10 1.14 1.44

Variables per cluster 147 1,808 348.23 147.00 25,421 MAX VALUE 405.11 348.43 1.00 1.44

Separator constraints 0 50,224 11,323.00 5,329.00 826,579 0 None 9,945.63 0.88 1.44

Separator variables 0 1,376 310.22 146.00 22,646 0 None 272.48 0.88 1.44

Clusters per variable 1 11 9.16 10.00 25,421 MAX VALUE 6,014.03 2.12 0.23 1.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5,475	86,728	14,098.00	5,475.00	1,029,150	MAX VALUE	671.28	16,032.10	1.14	1.44
Variables per cluster	147	1,808	348.23	147.00	25,421	MAX VALUE	405.11	348.43	1.00	1.44
Separator constraints	0	50,224	11,323.00	5,329.00	826,579	0	None	9,945.63	0.88	1.44
Separator variables	0	1,376	310.22	146.00	22,646	0	None	272.48	0.88	1.44
Clusters per variable	1	11	9.16	10.00	25,421	MAX VALUE	6,014.03	2.12	0.23	1.69

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 67,525
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-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 75.00 1.00 0.00 0.00 0.00 0.00

Degree 74 74 74.00 74.00 5,550 MAX VALUE 322.81 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 75 1 0.00 0.00 0.00 0.00

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	1.00	1.00	1.00	1.00	75.00	1.00	0.00	0.00	0.00	0.00
Degree	74	74	74.00	74.00	5,550	MAX VALUE	322.81	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	75	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 67,525

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

Clustering coefficient 1.00 1.00 1.00 1.00 75.00 1.00 0.00 0.00 0.00 0.00

Degree 74 74 74.00 74.00 5,550 MAX VALUE 322.81 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 75 1 0.00 0.00 0.00 0.00

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	1.00	1.00	1.00	1.00	75.00	1.00	0.00	0.00	0.00	0.00
Degree	74	74	74.00	74.00	5,550	MAX VALUE	322.81	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	75	1	0.00	0.00	0.00	0.00
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/langford3ExtConvert/normalized-langford-3-25-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-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: 0.14%
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 0.00 0.00 0.83 0.00 None 0.01 31.59 0.01

Degree 2 8 3.95 4.00 10,950 MAX VALUE 3,725.95 1.00 0.25 1.28

Eccentricity 14 27 18.88 19.00 52,405 MAX VALUE 8,137.04 2.13 0.11 2.10

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	0.00	0.00	0.83	0.00	None	0.01	31.59	0.01
Degree	2	8	3.95	4.00	10,950	MAX VALUE	3,725.95	1.00	0.25	1.28
Eccentricity	14	27	18.88	19.00	52,405	MAX VALUE	8,137.04	2.13	0.11	2.10
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: 3.95%

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

Clustering coefficient 0.47 1.00 0.82 0.80 2,275.62 0.00 -595.52 0.15 0.18 4.53

Degree 2 626 109.51 10.00 303,900 MAX VALUE 8,282.23 185.01 1.69 4.19

Eccentricity 4 6 4.88 5.00 13,532 MAX VALUE 4,376.43 0.58 0.12 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.80	2,275.62	0.00	-595.52	0.15	0.18	4.53
Degree	2	626	109.51	10.00	303,900	MAX VALUE	8,282.23	185.01	1.69	4.19
Eccentricity	4	6	4.88	5.00	13,532	MAX VALUE	4,376.43	0.58	0.12	0.88

Incidence graph

Density: 0.14%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-25-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 74 3.89 2.00 11,100 MAX VALUE 2,246.29 11.53 2.96 0.12

Eccentricity 3 4 3.97 4.00 11,325 MAX VALUE 3,929.36 0.16 0.04 0.12

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

XCSP 2.1 Benchmarks