XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-9-ext
Number of variables: 27
Number of constraints: 351
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 27
Number of constraints: 351

General features

Coarse blocks: 18,738
Value tables: 27

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

Arity 2 2 2.00 2.00 702 MAX VALUE 243.29 0.00 0.00 0.00

Coarse blocks size 1 26 24.99 26.00 468,288 MAX VALUE 58,587.10 4.92 0.20 0.17

Relational linkage 0.04 0.04 0.04 0.04 19.00 0.00 -1,690.76 0.00 0.00 0.00

Tightness 0.04 0.98 0.08 0.04 29.81 0.00 -1,098.04 0.21 2.43 0.31

Tuples 17 702 667.08 702.00 234,144 MAX VALUE 2,237.12 150.21 0.23 0.31

Values 27 27 27.00 27.00 729 MAX VALUE 88.99 0.00 0.00 0.00

Value table constraints 26 26 26.00 26.00 702 1.60e+38 87.97 0.00 0.00 0.00

Value table partitions 27 27 27.00 27.00 729 MAX VALUE 88.99 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	702	MAX VALUE	243.29	0.00	0.00	0.00
Coarse blocks size	1	26	24.99	26.00	468,288	MAX VALUE	58,587.10	4.92	0.20	0.17
Relational linkage	0.04	0.04	0.04	0.04	19.00	0.00	-1,690.76	0.00	0.00	0.00
Tightness	0.04	0.98	0.08	0.04	29.81	0.00	-1,098.04	0.21	2.43	0.31
Tuples	17	702	667.08	702.00	234,144	MAX VALUE	2,237.12	150.21	0.23	0.31
Values	27	27	27.00	27.00	729	MAX VALUE	88.99	0.00	0.00	0.00
Value table constraints	26	26	26.00	26.00	702	1.60e+38	87.97	0.00	0.00	0.00
Value table partitions	27	27	27.00	27.00	729	MAX VALUE	88.99	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/langford/normalized-langford-3-9-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Tree1.json

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

Cluster constraints 351 351 351.00 351.00 351 351 5.86 0.00 0.00 0.00

Variables per cluster 27 27 27.00 27.00 27 27 3.30 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 27 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	351	351	351.00	351.00	351	351	5.86	0.00
Variables per cluster	27	27	27.00	27.00	27	27	3.30	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	27	1	0.00	0.00

Dual tree decomposition

Number of clusters: 25
Number of leaves: 13
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/DualTree1.json

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

Cluster constraints 675 3,958 1,300.00 675.00 32,500 MAX VALUE 174.61 907.86 0.70 1.40

Variables per cluster 51 236 89.96 51.00 2,249 MAX VALUE 108.90 53.84 0.60 1.40

Separator constraints 0 2,250 949.00 625.00 23,725 0 None 515.87 0.54 1.40

Separator variables 0 180 75.92 50.00 1,898 0 None 41.27 0.54 1.40

Clusters per variable 1 8 6.41 7.00 2,249 MAX VALUE 627.35 1.79 0.28 1.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	675	3,958	1,300.00	675.00	32,500	MAX VALUE	174.61	907.86	0.70	1.40
Variables per cluster	51	236	89.96	51.00	2,249	MAX VALUE	108.90	53.84	0.60	1.40
Separator constraints	0	2,250	949.00	625.00	23,725	0	None	515.87	0.54	1.40
Separator variables	0	180	75.92	50.00	1,898	0	None	41.27	0.54	1.40
Clusters per variable	1	8	6.41	7.00	2,249	MAX VALUE	627.35	1.79	0.28	1.62

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,925
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-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 27.00 1.00 0.00 0.00 0.00 0.00

Degree 26 26 26.00 26.00 702 1.60e+38 87.97 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 27 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	27.00	1.00	0.00	0.00	0.00	0.00
Degree	26	26	26.00	26.00	702	1.60e+38	87.97	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	27	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: 2,925

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

Clustering coefficient 1.00 1.00 1.00 1.00 27.00 1.00 0.00 0.00 0.00 0.00

Degree 26 26 26.00 26.00 702 1.60e+38 87.97 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 27 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	27.00	1.00	0.00	0.00	0.00	0.00
Degree	26	26	26.00	26.00	702	1.60e+38	87.97	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	27	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: 14.29%
MCB compute time (ms): 4,027
MCB cycles: 8,425
Triangles: 73,125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 179.08 0.00 -236.20 0.00 0.00 0.00

Degree 50 50 50.00 50.00 17,550 MAX VALUE 1,373.12 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 702 MAX VALUE 243.29 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 25,275 MAX VALUE 9,255.81 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	179.08	0.00	-236.20
Degree	50	50	50.00	50.00	17,550	MAX VALUE	1,373.12
Eccentricity	2	2	2.00	2.00	702	MAX VALUE	243.29
MCB cycle size	3	3	3.00	3.00	25,275	MAX VALUE	9,255.81

Minimal dual graph

Density: 1.10%
MCB compute time (ms): 985
MCB cycles: 326

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

Clustering coefficient 0.00 0.10 0.00 0.00 0.23 0.00 None 0.01 10.99 0.05

Degree 2 7 3.85 4.00 1,350 MAX VALUE 462.66 0.96 0.25 1.25

Eccentricity 7 11 8.87 9.00 3,115 MAX VALUE 764.77 0.83 0.09 1.23

MCB cycle size 3 9 6.03 6.00 1,965 MAX VALUE 577.64 1.28 0.21 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.10	0.00	0.00	0.23	0.00	None	0.01	10.99	0.05
Degree	2	7	3.85	4.00	1,350	MAX VALUE	462.66	0.96	0.25	1.25
Eccentricity	7	11	8.87	9.00	3,115	MAX VALUE	764.77	0.83	0.09	1.23
MCB cycle size	3	9	6.03	6.00	1,965	MAX VALUE	577.64	1.28	0.21	1.55

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: 9.18%

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

Clustering coefficient 0.53 1.00 0.80 0.75 282.21 0.00 -83.07 0.15 0.19 3.75

Degree 2 119 32.13 9.00 11,276 MAX VALUE 912.68 38.67 1.20 3.50

Eccentricity 3 6 4.25 4.00 1,493 MAX VALUE 504.50 0.60 0.14 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.53	1.00	0.80	0.75	282.21	0.00	-83.07	0.15	0.19	3.75
Degree	2	119	32.13	9.00	11,276	MAX VALUE	912.68	38.67	1.20	3.50
Eccentricity	3	6	4.25	4.00	1,493	MAX VALUE	504.50	0.60	0.14	0.91

Incidence graph

Density: 0.99%
MCB compute time (ms): 153
MCB cycles: 325
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-9-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 26 3.71 2.00 1,404 MAX VALUE 331.26 6.18 1.66 0.26

Eccentricity 3 4 3.93 4.00 1,485 MAX VALUE 516.25 0.26 0.07 0.26

MCB cycle size 6 6 6.00 6.00 1,950 MAX VALUE 582.32 0.00 0.00 0.00

XCSP 2.1 Benchmarks