XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-18-ext
Number of variables: 54
Number of constraints: 1431
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 54
Number of constraints: 1431

General features

Coarse blocks: 153,792
Value tables: 54

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

Arity 2 2 2.00 2.00 2,862 MAX VALUE 991.89 0.00 0.00 0.00

Coarse blocks size 1 53 51.94 53.00 7,988,110 MAX VALUE 598,164.00 7.34 0.14 0.10

Relational linkage 0.02 0.02 0.02 0.02 40.00 0.00 -8,616.21 0.00 0.00 0.00

Tightness 0.02 0.99 0.04 0.02 61.30 0.00 -5,565.17 0.15 3.53 0.19

Tuples 35 2,862 2,791.09 2,862.00 3,994,060 MAX VALUE 11,238.70 441.38 0.16 0.19

Values 54 54 54.00 54.00 2,916 MAX VALUE 215.41 0.00 0.00 0.00

Value table constraints 53 53 53.00 53.00 2,862 MAX VALUE 214.40 0.00 0.00 0.00

Value table partitions 54 54 54.00 54.00 2,916 MAX VALUE 215.41 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	2,862	MAX VALUE	991.89	0.00	0.00	0.00
Coarse blocks size	1	53	51.94	53.00	7,988,110	MAX VALUE	598,164.00	7.34	0.14	0.10
Relational linkage	0.02	0.02	0.02	0.02	40.00	0.00	-8,616.21	0.00	0.00	0.00
Tightness	0.02	0.99	0.04	0.02	61.30	0.00	-5,565.17	0.15	3.53	0.19
Tuples	35	2,862	2,791.09	2,862.00	3,994,060	MAX VALUE	11,238.70	441.38	0.16	0.19
Values	54	54	54.00	54.00	2,916	MAX VALUE	215.41	0.00	0.00	0.00
Value table constraints	53	53	53.00	53.00	2,862	MAX VALUE	214.40	0.00	0.00	0.00
Value table partitions	54	54	54.00	54.00	2,916	MAX VALUE	215.41	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-3-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Tree1.json

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

Cluster constraints 1,431 1,431 1,431.00 1,431.00 1,431 1,431 7.27 0.00 0.00 0.00

Variables per cluster 54 54 54.00 54.00 54 54 3.99 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 54 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	1,431	1,431	1,431.00	1,431.00	1,431	1,431	7.27	0.00
Variables per cluster	54	54	54.00	54.00	54	54	3.99	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	54	1	0.00	0.00

Dual tree decomposition

Number of clusters: 52
Number of leaves: 27
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/DualTree1.json

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

Cluster constraints 2,808 32,608 6,631.00 2,808.00 344,812 MAX VALUE 441.87 6,532.04 0.99 1.37

Variables per cluster 105 944 227.52 105.00 11,831 MAX VALUE 269.21 196.23 0.86 1.37

Separator constraints 0 18,720 5,200.00 2,704.00 270,400 0 None 3,947.79 0.76 1.37

Separator variables 0 720 200.00 104.00 10,400 0 None 151.84 0.76 1.37

Clusters per variable 1 10 8.27 9.00 11,831 MAX VALUE 2,944.63 2.04 0.25 1.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2,808	32,608	6,631.00	2,808.00	344,812	MAX VALUE	441.87	6,532.04	0.99	1.37
Variables per cluster	105	944	227.52	105.00	11,831	MAX VALUE	269.21	196.23	0.86	1.37
Separator constraints	0	18,720	5,200.00	2,704.00	270,400	0	None	3,947.79	0.76	1.37
Separator variables	0	720	200.00	104.00	10,400	0	None	151.84	0.76	1.37
Clusters per variable	1	10	8.27	9.00	11,831	MAX VALUE	2,944.63	2.04	0.25	1.69

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 24,804
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-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 54.00 1.00 0.00 0.00 0.00 0.00

Degree 53 53 53.00 53.00 2,862 MAX VALUE 214.40 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 54 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	54.00	1.00	0.00	0.00	0.00	0.00
Degree	53	53	53.00	53.00	2,862	MAX VALUE	214.40	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	54	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: 24,804

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

Clustering coefficient 1.00 1.00 1.00 1.00 54.00 1.00 0.00 0.00 0.00 0.00

Degree 53 53 53.00 53.00 2,862 MAX VALUE 214.40 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 54 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	54.00	1.00	0.00	0.00	0.00	0.00
Degree	53	53	53.00	53.00	2,862	MAX VALUE	214.40	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	54	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): 221,494
MCB cycles: 72,982
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-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 3 3 3.00 3.00 218,946 MAX VALUE 80,178.90 0.00 0.00 0.00

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	3	3	3.00	3.00	218,946	MAX VALUE	80,178.90	0.00	0.00	0.00

Minimal dual graph

Density: 0.27%
MCB compute time (ms): 54,178
MCB cycles: 1,382

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 22.68 0.02

Degree 2 7 3.92 4.00 5,616 MAX VALUE 1,914.47 0.98 0.25 1.27

Eccentricity 11 20 15.08 15.00 21,584 MAX VALUE 3,874.91 1.63 0.11 1.88

MCB cycle size 3 18 6.09 7.00 8,419 MAX VALUE 2,466.39 1.25 0.20 1.42

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	22.68	0.02
Degree	2	7	3.92	4.00	5,616	MAX VALUE	1,914.47	0.98	0.25	1.27
Eccentricity	11	20	15.08	15.00	21,584	MAX VALUE	3,874.91	1.63	0.11	1.88
MCB cycle size	3	18	6.09	7.00	8,419	MAX VALUE	2,466.39	1.25	0.20	1.42

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: 5.04%

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

Clustering coefficient 0.47 1.00 0.82 0.78 1,166.95 0.00 -315.98 0.15 0.18 4.28

Degree 2 361 72.06 9.00 103,120 MAX VALUE 4,102.63 111.05 1.54 3.93

Eccentricity 3 6 4.48 4.00 6,412 MAX VALUE 2,131.85 0.62 0.14 0.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.78	1,166.95	0.00	-315.98	0.15	0.18	4.28
Degree	2	361	72.06	9.00	103,120	MAX VALUE	4,102.63	111.05	1.54	3.93
Eccentricity	3	6	4.48	4.00	6,412	MAX VALUE	2,131.85	0.62	0.14	0.94

Incidence graph

Density: 0.26%
MCB compute time (ms): 3,536
MCB cycles: 1,378
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-18-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 53 3.85 2.00 5,724 MAX VALUE 1,206.29 9.55 2.48 0.16

Eccentricity 3 4 3.96 4.00 5,886 MAX VALUE 2,043.11 0.19 0.05 0.16

MCB cycle size 6 6 6.00 6.00 8,268 MAX VALUE 2,469.04 0.00 0.00 0.00

XCSP 2.1 Benchmarks