XCSP 2.1 Benchmark Database

Instance: normalized-langford-2-14-ext
Number of variables: 28
Number of constraints: 378
Satisfiable: True
Timestamp: 2025-07-27 21:34:22
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 28
Number of constraints: 378

General features

Coarse blocks: 20,930
Value tables: 28

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

Arity 2 2 2.00 2.00 756 MAX VALUE 262.01 0.00 0.00 0.00

Coarse blocks size 1 27 26.32 27.00 550,914 MAX VALUE 67,182.30 4.14 0.16 0.12

Relational linkage 0.04 0.04 0.04 0.04 19.50 0.00 -1,819.38 0.00 0.00 0.00

Tightness 0.04 0.98 0.07 0.04 26.65 0.00 -1,213.28 0.18 2.52 0.26

Tuples 13 756 728.72 756.00 275,457 MAX VALUE 2,453.88 139.09 0.19 0.26

Values 28 28 28.00 28.00 784 MAX VALUE 93.30 0.00 0.00 0.00

Value table constraints 27 27 27.00 27.00 756 MAX VALUE 92.28 0.00 0.00 0.00

Value table partitions 28 28 28.00 28.00 784 MAX VALUE 93.30 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	756	MAX VALUE	262.01	0.00	0.00	0.00
Coarse blocks size	1	27	26.32	27.00	550,914	MAX VALUE	67,182.30	4.14	0.16	0.12
Relational linkage	0.04	0.04	0.04	0.04	19.50	0.00	-1,819.38	0.00	0.00	0.00
Tightness	0.04	0.98	0.07	0.04	26.65	0.00	-1,213.28	0.18	2.52	0.26
Tuples	13	756	728.72	756.00	275,457	MAX VALUE	2,453.88	139.09	0.19	0.26
Values	28	28	28.00	28.00	784	MAX VALUE	93.30	0.00	0.00	0.00
Value table constraints	27	27	27.00	27.00	756	MAX VALUE	92.28	0.00	0.00	0.00
Value table partitions	28	28	28.00	28.00	784	MAX VALUE	93.30	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-2-14-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Tree1.json

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

Cluster constraints 378 378 378.00 378.00 378 378 5.93 0.00 0.00 0.00

Variables per cluster 28 28 28.00 28.00 28 28 3.33 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 28 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	378	378	378.00	378.00	378	378	5.93	0.00
Variables per cluster	28	28	28.00	28.00	28	28	3.33	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	28	1	0.00	0.00

Dual tree decomposition

Number of clusters: 26
Number of leaves: 14
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/DualTree1.json

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

Cluster constraints 728 4,480 1,414.00 728.00 36,764 MAX VALUE 183.59 1,012.04 0.72 1.19

Variables per cluster 53 256 94.23 53.00 2,450 MAX VALUE 114.29 57.88 0.61 1.19

Separator constraints 0 2,496 1,036.00 676.00 26,936 0 None 575.25 0.56 1.19

Separator variables 0 192 79.69 52.00 2,072 0 None 44.25 0.56 1.19

Clusters per variable 1 8 6.48 7.00 2,450 MAX VALUE 680.60 1.78 0.28 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	728	4,480	1,414.00	728.00	36,764	MAX VALUE	183.59	1,012.04	0.72	1.19
Variables per cluster	53	256	94.23	53.00	2,450	MAX VALUE	114.29	57.88	0.61	1.19
Separator constraints	0	2,496	1,036.00	676.00	26,936	0	None	575.25	0.56	1.19
Separator variables	0	192	79.69	52.00	2,072	0	None	44.25	0.56	1.19
Clusters per variable	1	8	6.48	7.00	2,450	MAX VALUE	680.60	1.78	0.28	1.52

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 3,276
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-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 28.00 1.00 0.00 0.00 0.00 0.00

Degree 27 27 27.00 27.00 756 MAX VALUE 92.28 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 28 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	28.00	1.00	0.00	0.00	0.00	0.00
Degree	27	27	27.00	27.00	756	MAX VALUE	92.28	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	28	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: 3,276

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

Clustering coefficient 1.00 1.00 1.00 1.00 28.00 1.00 0.00 0.00 0.00 0.00

Degree 27 27 27.00 27.00 756 MAX VALUE 92.28 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 28 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	28.00	1.00	0.00	0.00	0.00	0.00
Degree	27	27	27.00	27.00	756	MAX VALUE	92.28	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	28	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: 13.79%
MCB compute time (ms): 5,035
MCB cycles: 9,451
Triangles: 85,176
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 192.71 0.00 -254.67 0.00 0.00 0.00

Degree 52 52 52.00 52.00 19,656 MAX VALUE 1,493.57 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 756 MAX VALUE 262.01 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 28,353 MAX VALUE 10,383.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)
Clustering coefficient	0.51	0.51	0.51	0.51	192.71	0.00	-254.67
Degree	52	52	52.00	52.00	19,656	MAX VALUE	1,493.57
Eccentricity	2	2	2.00	2.00	756	MAX VALUE	262.01
MCB cycle size	3	3	3.00	3.00	28,353	MAX VALUE	10,383.00

Minimal dual graph

Density: 1.02%
MCB compute time (ms): 1,030
MCB cycles: 353

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 0.03 11.62 0.05

Degree 2 7 3.85 4.00 1,456 MAX VALUE 499.30 0.93 0.24 1.24

Eccentricity 8 12 10.03 10.00 3,791 MAX VALUE 869.82 0.94 0.09 1.35

MCB cycle size 3 13 5.94 6.00 2,096 MAX VALUE 621.91 1.15 0.19 1.39

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	0.03	11.62	0.05
Degree	2	7	3.85	4.00	1,456	MAX VALUE	499.30	0.93	0.24	1.24
Eccentricity	8	12	10.03	10.00	3,791	MAX VALUE	869.82	0.94	0.09	1.35
MCB cycle size	3	13	5.94	6.00	2,096	MAX VALUE	621.91	1.15	0.19	1.39

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: 8.73%

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

Clustering coefficient 0.47 1.00 0.81 0.76 304.45 0.00 -88.79 0.15 0.19 3.70

Degree 2 121 32.90 9.00 12,438 MAX VALUE 983.26 40.51 1.23 3.50

Eccentricity 3 5 3.87 4.00 1,463 MAX VALUE 507.54 0.56 0.14 0.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.76	304.45	0.00	-88.79	0.15	0.19	3.70
Degree	2	121	32.90	9.00	12,438	MAX VALUE	983.26	40.51	1.23	3.50
Eccentricity	3	5	3.87	4.00	1,463	MAX VALUE	507.54	0.56	0.14	0.83

Incidence graph

Density: 0.92%
MCB compute time (ms): 190
MCB cycles: 351
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-14-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 27 3.72 2.00 1,512 MAX VALUE 354.29 6.33 1.70 0.25

Eccentricity 3 4 3.93 4.00 1,596 MAX VALUE 554.78 0.25 0.06 0.25

MCB cycle size 6 6 6.00 6.00 2,106 MAX VALUE 628.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks