XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-8-ext
Number of variables: 24
Number of constraints: 276
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 24
Number of constraints: 276

General features

Coarse blocks: 13,072
Value tables: 24

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

Arity 2 2 2.00 2.00 552 MAX VALUE 191.31 0.00 0.00 0.00

Coarse blocks size 1 23 22.00 23.00 287,632 MAX VALUE 39,131.00 4.57 0.21 0.18

Relational linkage 0.04 0.04 0.04 0.04 16.67 0.00 -1,271.22 0.00 0.00 0.00

Tightness 0.04 0.97 0.10 0.04 26.32 0.00 -826.82 0.22 2.27 0.34

Tuples 15 552 521.07 552.00 143,816 MAX VALUE 1,688.08 124.67 0.24 0.34

Values 24 24 24.00 24.00 576 1.33e+33 76.27 0.00 0.00 0.00

Value table constraints 23 23 23.00 23.00 552 4.80e+32 75.25 0.00 0.00 0.00

Value table partitions 24 24 24.00 24.00 576 1.33e+33 76.27 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	552	MAX VALUE	191.31	0.00	0.00	0.00
Coarse blocks size	1	23	22.00	23.00	287,632	MAX VALUE	39,131.00	4.57	0.21	0.18
Relational linkage	0.04	0.04	0.04	0.04	16.67	0.00	-1,271.22	0.00	0.00	0.00
Tightness	0.04	0.97	0.10	0.04	26.32	0.00	-826.82	0.22	2.27	0.34
Tuples	15	552	521.07	552.00	143,816	MAX VALUE	1,688.08	124.67	0.24	0.34
Values	24	24	24.00	24.00	576	1.33e+33	76.27	0.00	0.00	0.00
Value table constraints	23	23	23.00	23.00	552	4.80e+32	75.25	0.00	0.00	0.00
Value table partitions	24	24	24.00	24.00	576	1.33e+33	76.27	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-3-8-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Tree1.json

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

Cluster constraints 276 276 276.00 276.00 276 276 5.62 0.00 0.00 0.00

Variables per cluster 24 24 24.00 24.00 24 24 3.18 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 24 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	276	276	276.00	276.00	276	276	5.62	0.00
Variables per cluster	24	24	24.00	24.00	24	24	3.18	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	24	1	0.00	0.00

Dual tree decomposition

Number of clusters: 22
Number of leaves: 12
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/DualTree1.json

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

Cluster constraints 528 2,512 980.00 528.00 21,560 MAX VALUE 147.76 643.94 0.66 1.12

Variables per cluster 45 176 76.55 45.00 1,684 MAX VALUE 92.55 43.25 0.57 1.12

Separator constraints 0 1,584 704.00 484.00 15,488 0 None 370.99 0.53 1.18

Separator variables 0 144 64.00 44.00 1,408 0 None 33.73 0.53 1.18

Clusters per variable 1 8 6.10 6.00 1,684 MAX VALUE 478.83 1.77 0.29 1.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	528	2,512	980.00	528.00	21,560	MAX VALUE	147.76	643.94	0.66	1.12
Variables per cluster	45	176	76.55	45.00	1,684	MAX VALUE	92.55	43.25	0.57	1.12
Separator constraints	0	1,584	704.00	484.00	15,488	0	None	370.99	0.53	1.18
Separator variables	0	144	64.00	44.00	1,408	0	None	33.73	0.53	1.18
Clusters per variable	1	8	6.10	6.00	1,684	MAX VALUE	478.83	1.77	0.29	1.64

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,024
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-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 24.00 1.00 0.00 0.00 0.00 0.00

Degree 23 23 23.00 23.00 552 4.80e+32 75.25 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 24 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	24.00	1.00	0.00	0.00	0.00	0.00
Degree	23	23	23.00	23.00	552	4.80e+32	75.25	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	24	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: 2,024

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

Clustering coefficient 1.00 1.00 1.00 1.00 24.00 1.00 0.00 0.00 0.00 0.00

Degree 23 23 23.00 23.00 552 4.80e+32 75.25 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 24 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	24.00	1.00	0.00	0.00	0.00	0.00
Degree	23	23	23.00	23.00	552	4.80e+32	75.25	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	24	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: 16.00%
MCB compute time (ms): 1,791
MCB cycles: 5,797
Triangles: 44,528
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 141.21 0.00 -184.96 0.00 0.00 0.00

Degree 44 44 44.00 44.00 12,144 MAX VALUE 1,044.44 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 552 MAX VALUE 191.31 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 17,391 MAX VALUE 6,368.66 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	141.21	0.00	-184.96
Degree	44	44	44.00	44.00	12,144	MAX VALUE	1,044.44
Eccentricity	2	2	2.00	2.00	552	MAX VALUE	191.31
MCB cycle size	3	3	3.00	3.00	17,391	MAX VALUE	6,368.66

Minimal dual graph

Density: 1.39%
MCB compute time (ms): 372
MCB cycles: 255

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 9.92 0.07

Degree 2 6 3.83 4.00 1,056 MAX VALUE 362.88 0.91 0.24 1.22

Eccentricity 7 11 8.97 9.00 2,475 MAX VALUE 604.10 0.87 0.10 1.27

MCB cycle size 3 12 5.89 6.00 1,503 MAX VALUE 447.53 1.13 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	9.92	0.07
Degree	2	6	3.83	4.00	1,056	MAX VALUE	362.88	0.91	0.24	1.22
Eccentricity	7	11	8.97	9.00	2,475	MAX VALUE	604.10	0.87	0.10	1.27
MCB cycle size	3	12	5.89	6.00	1,503	MAX VALUE	447.53	1.13	0.19	1.39

Triangulated dual graph

Density: 72.00%
Triangles: 1,681,090

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

Clustering coefficient 0.82 1.00 0.89 0.90 244.81 0.00 -33.59 0.05 0.06 1.78

Degree 44 249 198.00 217.00 54,648 MAX VALUE 1,440.48 57.33 0.29 1.78

Eccentricity 2 2 2.00 2.00 552 MAX VALUE 191.31 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.82	1.00	0.89	0.90	244.81	0.00	-33.59	0.05	0.06	1.78
Degree	44	249	198.00	217.00	54,648	MAX VALUE	1,440.48	57.33	0.29	1.78
Eccentricity	2	2	2.00	2.00	552	MAX VALUE	191.31	0.00	0.00	0.00

Triangulated minimal dual graph

Density: 9.79%

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

Clustering coefficient 0.47 1.00 0.80 0.74 219.69 0.00 -68.74 0.16 0.20 3.65

Degree 2 94 26.92 9.00 7,430 MAX VALUE 697.75 30.65 1.14 3.39

Eccentricity 3 5 4.01 4.00 1,107 MAX VALUE 380.25 0.59 0.15 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.80	0.74	219.69	0.00	-68.74	0.16	0.20	3.65
Degree	2	94	26.92	9.00	7,430	MAX VALUE	697.75	30.65	1.14	3.39
Eccentricity	3	5	4.01	4.00	1,107	MAX VALUE	380.25	0.59	0.15	0.89

Incidence graph

Density: 1.23%
MCB compute time (ms): 87
MCB cycles: 253
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-8-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 23 3.68 2.00 1,104 MAX VALUE 266.56 5.70 1.55 0.28

Eccentricity 3 4 3.92 4.00 1,176 MAX VALUE 408.98 0.27 0.07 0.28

MCB cycle size 6 6 6.00 6.00 1,518 MAX VALUE 453.31 0.00 0.00 0.00

XCSP 2.1 Benchmarks