XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-21-ext
Number of variables: 63
Number of constraints: 1953
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 63
Number of constraints: 1953

General features

Coarse blocks: 245,070
Value tables: 63

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

Arity 2 2 2.00 2.00 3,906 MAX VALUE 1,353.72 0.00 0.00 0.00

Coarse blocks size 1 62 60.93 62.00 14,933,000 MAX VALUE 993,756.00 7.99 0.13 0.09

Relational linkage 0.02 0.02 0.02 0.02 47.00 0.00 -12,267.80 0.00 0.00 0.00

Tightness 0.02 0.99 0.04 0.02 71.79 0.00 -7,918.07 0.14 3.83 0.17

Tuples 41 3,906 3,823.10 3,906.00 7,466,510 MAX VALUE 15,969.30 559.21 0.15 0.17

Values 63 63 63.00 63.00 3,969 MAX VALUE 261.02 0.00 0.00 0.00

Value table constraints 62 62 62.00 62.00 3,906 MAX VALUE 260.01 0.00 0.00 0.00

Value table partitions 63 63 63.00 63.00 3,969 MAX VALUE 261.02 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	3,906	MAX VALUE	1,353.72	0.00	0.00	0.00
Coarse blocks size	1	62	60.93	62.00	14,933,000	MAX VALUE	993,756.00	7.99	0.13	0.09
Relational linkage	0.02	0.02	0.02	0.02	47.00	0.00	-12,267.80	0.00	0.00	0.00
Tightness	0.02	0.99	0.04	0.02	71.79	0.00	-7,918.07	0.14	3.83	0.17
Tuples	41	3,906	3,823.10	3,906.00	7,466,510	MAX VALUE	15,969.30	559.21	0.15	0.17
Values	63	63	63.00	63.00	3,969	MAX VALUE	261.02	0.00	0.00	0.00
Value table constraints	62	62	62.00	62.00	3,906	MAX VALUE	260.01	0.00	0.00	0.00
Value table partitions	63	63	63.00	63.00	3,969	MAX VALUE	261.02	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-3-21-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Tree1.json

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

Cluster constraints 1,953 1,953 1,953.00 1,953.00 1,953 1,953 7.58 0.00 0.00 0.00

Variables per cluster 63 63 63.00 63.00 63 63 4.14 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 63 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	1,953	1,953	1,953.00	1,953.00	1,953	1,953	7.58	0.00
Variables per cluster	63	63	63.00	63.00	63	63	4.14	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	63	1	0.00	0.00

Dual tree decomposition

Number of clusters: 61
Number of leaves: 31
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/DualTree1.json

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

Cluster constraints 3,843 49,968 9,424.00 3,843.00 574,864 MAX VALUE 538.34 9,938.36 1.05 1.42

Variables per cluster 123 1,248 276.97 123.00 16,895 MAX VALUE 326.46 255.45 0.92 1.42

Separator constraints 0 30,256 7,471.00 3,721.00 455,731 0 None 6,020.77 0.81 1.42

Separator variables 0 992 244.95 122.00 14,942 0 None 197.40 0.81 1.42

Clusters per variable 1 10 8.65 9.00 16,895 MAX VALUE 4,116.07 2.03 0.23 1.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3,843	49,968	9,424.00	3,843.00	574,864	MAX VALUE	538.34	9,938.36	1.05	1.42
Variables per cluster	123	1,248	276.97	123.00	16,895	MAX VALUE	326.46	255.45	0.92	1.42
Separator constraints	0	30,256	7,471.00	3,721.00	455,731	0	None	6,020.77	0.81	1.42
Separator variables	0	992	244.95	122.00	14,942	0	None	197.40	0.81	1.42
Clusters per variable	1	10	8.65	9.00	16,895	MAX VALUE	4,116.07	2.03	0.23	1.38

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 39,711
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-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 63.00 1.00 0.00 0.00 0.00 0.00

Degree 62 62 62.00 62.00 3,906 MAX VALUE 260.01 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 63 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	63.00	1.00	0.00	0.00	0.00	0.00
Degree	62	62	62.00	62.00	3,906	MAX VALUE	260.01	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	63	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: 39,711

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

Clustering coefficient 1.00 1.00 1.00 1.00 63.00 1.00 0.00 0.00 0.00 0.00

Degree 62 62 62.00 62.00 3,906 MAX VALUE 260.01 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 63 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	63.00	1.00	0.00	0.00	0.00	0.00
Degree	62	62	62.00	62.00	3,906	MAX VALUE	260.01	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	63	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-3-21-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-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: 0.20%
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 26.50 0.01

Degree 2 8 3.94 4.00 7,686 MAX VALUE 2,617.63 0.99 0.25 1.28

Eccentricity 13 23 16.70 17.00 32,624 MAX VALUE 5,487.06 1.88 0.11 2.00

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	0.00	0.33	0.00	0.00	0.83	0.00	None	0.01	26.50	0.01
Degree	2	8	3.94	4.00	7,686	MAX VALUE	2,617.63	0.99	0.25	1.28
Eccentricity	13	23	16.70	17.00	32,624	MAX VALUE	5,487.06	1.88	0.11	2.00
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: 4.54%

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

Clustering coefficient 0.47 1.00 0.82 0.78 1,596.27 0.00 -426.17 0.15 0.18 4.43

Degree 2 457 88.71 9.00 173,248 MAX VALUE 5,731.18 142.13 1.60 4.06

Eccentricity 3 6 4.60 5.00 8,992 MAX VALUE 2,965.86 0.59 0.13 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.78	1,596.27	0.00	-426.17	0.15	0.18	4.43
Degree	2	457	88.71	9.00	173,248	MAX VALUE	5,731.18	142.13	1.60	4.06
Eccentricity	3	6	4.60	5.00	8,992	MAX VALUE	2,965.86	0.59	0.13	0.88

Incidence graph

Density: 0.19%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-21-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 62 3.88 2.00 7,812 MAX VALUE 1,613.73 10.44 2.69 0.14

Eccentricity 3 4 3.97 4.00 8,001 MAX VALUE 2,776.65 0.17 0.04 0.14

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

XCSP 2.1 Benchmarks