XCSP 2.1 Benchmark Database

Instance: normalized-langford-2-40-ext
Number of variables: 80
Number of constraints: 3160
Satisfiable: True
Timestamp: 2025-07-27 21:34:22
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 80
Number of constraints: 3160

General features

Coarse blocks: 503,880
Value tables: 80

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

Arity 2 2 2.00 2.00 6,320 MAX VALUE 2,190.35 0.00 0.00 0.00

Coarse blocks size 1 79 78.28 79.00 39,441,500 MAX VALUE 2,181,230.00 7.48 0.10 0.05

Relational linkage 0.01 0.01 0.01 0.01 58.50 0.00 -20,507.90 0.00 0.00 0.00

Tightness 0.01 0.99 0.02 0.01 78.63 0.00 -13,672.30 0.11 4.40 0.11

Tuples 39 6,320 6,240.74 6,320.00 19,720,700 MAX VALUE 27,466.60 700.00 0.11 0.11

Values 80 80 80.00 80.00 6,400 MAX VALUE 350.56 0.00 0.00 0.00

Value table constraints 79 79 79.00 79.00 6,320 MAX VALUE 349.56 0.00 0.00 0.00

Value table partitions 80 80 80.00 80.00 6,400 MAX VALUE 350.56 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	6,320	MAX VALUE	2,190.35	0.00	0.00	0.00
Coarse blocks size	1	79	78.28	79.00	39,441,500	MAX VALUE	2,181,230.00	7.48	0.10	0.05
Relational linkage	0.01	0.01	0.01	0.01	58.50	0.00	-20,507.90	0.00	0.00	0.00
Tightness	0.01	0.99	0.02	0.01	78.63	0.00	-13,672.30	0.11	4.40	0.11
Tuples	39	6,320	6,240.74	6,320.00	19,720,700	MAX VALUE	27,466.60	700.00	0.11	0.11
Values	80	80	80.00	80.00	6,400	MAX VALUE	350.56	0.00	0.00	0.00
Value table constraints	79	79	79.00	79.00	6,320	MAX VALUE	349.56	0.00	0.00	0.00
Value table partitions	80	80	80.00	80.00	6,400	MAX VALUE	350.56	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/langford2ExtConvert/normalized-langford-2-40-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Tree1.json

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

Cluster constraints 3,160 3,160 3,160.00 3,160.00 3,160 3,160 8.06 0.00 0.00 0.00

Variables per cluster 80 80 80.00 80.00 80 80 4.38 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 80 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	3,160	3,160	3,160.00	3,160.00	3,160	3,160	8.06	0.00
Variables per cluster	80	80	80.00	80.00	80	80	4.38	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	80	1	0.00	0.00

Dual tree decomposition

Number of clusters: 78
Number of leaves: 40
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/DualTree1.json

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

Cluster constraints 6,240 104,448 16,296.00 6,240.00 1,271,090 MAX VALUE 727.65 19,088.00 1.17 1.28

Variables per cluster 157 2,048 377.33 157.00 29,432 MAX VALUE 438.25 389.24 1.03 1.28

Separator constraints 0 59,904 13,136.00 6,084.00 1,024,610 0 None 11,891.80 0.91 1.28

Separator variables 0 1,536 336.82 156.00 26,272 0 None 304.92 0.91 1.28

Clusters per variable 1 11 9.31 10.00 29,432 MAX VALUE 6,906.36 2.11 0.23 1.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6,240	104,448	16,296.00	6,240.00	1,271,090	MAX VALUE	727.65	19,088.00	1.17	1.28
Variables per cluster	157	2,048	377.33	157.00	29,432	MAX VALUE	438.25	389.24	1.03	1.28
Separator constraints	0	59,904	13,136.00	6,084.00	1,024,610	0	None	11,891.80	0.91	1.28
Separator variables	0	1,536	336.82	156.00	26,272	0	None	304.92	0.91	1.28
Clusters per variable	1	11	9.31	10.00	29,432	MAX VALUE	6,906.36	2.11	0.23	1.56

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 82,160
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-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 80.00 1.00 0.00 0.00 0.00 0.00

Degree 79 79 79.00 79.00 6,320 MAX VALUE 349.56 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 80 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	80.00	1.00	0.00	0.00	0.00	0.00
Degree	79	79	79.00	79.00	6,320	MAX VALUE	349.56	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	80	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: 82,160

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

Clustering coefficient 1.00 1.00 1.00 1.00 80.00 1.00 0.00 0.00 0.00 0.00

Degree 79 79 79.00 79.00 6,320 MAX VALUE 349.56 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 80 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	80.00	1.00	0.00	0.00	0.00	0.00
Degree	79	79	79.00	79.00	6,320	MAX VALUE	349.56	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	80	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/langford2ExtConvert/normalized-langford-2-40-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-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: 0.13%
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 33.71 0.01

Degree 2 8 3.95 4.00 12,480 MAX VALUE 4,245.24 1.00 0.25 1.28

Eccentricity 15 27 19.69 19.00 62,230 MAX VALUE 9,397.80 2.26 0.11 2.15

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	33.71	0.01
Degree	2	8	3.95	4.00	12,480	MAX VALUE	4,245.24	1.00	0.25	1.28
Eccentricity	15	27	19.69	19.00	62,230	MAX VALUE	9,397.80	2.26	0.11	2.15
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: 3.70%

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

Clustering coefficient 0.47 1.00 0.82 0.80 2,594.61 0.00 -675.99 0.15 0.18 4.53

Degree 2 706 116.84 9.00 369,220 MAX VALUE 9,460.68 202.28 1.73 4.17

Eccentricity 4 6 4.83 5.00 15,268 MAX VALUE 4,954.46 0.58 0.12 0.87

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.80	2,594.61	0.00	-675.99	0.15	0.18	4.53
Degree	2	706	116.84	9.00	369,220	MAX VALUE	9,460.68	202.28	1.73	4.17
Eccentricity	4	6	4.83	5.00	15,268	MAX VALUE	4,954.46	0.58	0.12	0.87

Incidence graph

Density: 0.12%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-40-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 79 3.90 2.00 12,640 MAX VALUE 2,539.90 11.95 3.06 0.12

Eccentricity 3 4 3.98 4.00 12,880 MAX VALUE 4,468.58 0.16 0.04 0.12

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

XCSP 2.1 Benchmarks