XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-16-ext
Number of variables: 48
Number of constraints: 1128
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 48
Number of constraints: 1128

General features

Coarse blocks: 107,680
Value tables: 48

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

Arity 2 2 2.00 2.00 2,256 MAX VALUE 781.87 0.00 0.00 0.00

Coarse blocks size 1 47 45.95 47.00 4,947,620 MAX VALUE 405,097.00 6.88 0.15 0.11

Relational linkage 0.02 0.02 0.02 0.02 35.33 0.00 -6,565.56 0.00 0.00 0.00

Tightness 0.02 0.99 0.05 0.02 54.30 0.00 -4,243.38 0.16 3.32 0.21

Tuples 31 2,256 2,193.09 2,256.00 2,473,810 MAX VALUE 8,579.19 368.16 0.17 0.21

Values 48 48 48.00 48.00 2,304 MAX VALUE 185.82 0.00 0.00 0.00

Value table constraints 47 47 47.00 47.00 2,256 MAX VALUE 184.81 0.00 0.00 0.00

Value table partitions 48 48 48.00 48.00 2,304 MAX VALUE 185.82 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	2,256	MAX VALUE	781.87	0.00	0.00	0.00
Coarse blocks size	1	47	45.95	47.00	4,947,620	MAX VALUE	405,097.00	6.88	0.15	0.11
Relational linkage	0.02	0.02	0.02	0.02	35.33	0.00	-6,565.56	0.00	0.00	0.00
Tightness	0.02	0.99	0.05	0.02	54.30	0.00	-4,243.38	0.16	3.32	0.21
Tuples	31	2,256	2,193.09	2,256.00	2,473,810	MAX VALUE	8,579.19	368.16	0.17	0.21
Values	48	48	48.00	48.00	2,304	MAX VALUE	185.82	0.00	0.00	0.00
Value table constraints	47	47	47.00	47.00	2,256	MAX VALUE	184.81	0.00	0.00	0.00
Value table partitions	48	48	48.00	48.00	2,304	MAX VALUE	185.82	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-3-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Tree1.json

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

Cluster constraints 1,128 1,128 1,128.00 1,128.00 1,128 1,128 7.03 0.00 0.00 0.00

Variables per cluster 48 48 48.00 48.00 48 48 3.87 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 48 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	1,128	1,128	1,128.00	1,128.00	1,128	1,128	7.03	0.00
Variables per cluster	48	48	48.00	48.00	48	48	3.87	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	48	1	0.00	0.00

Dual tree decomposition

Number of clusters: 46
Number of leaves: 24
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/DualTree1.json

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

Cluster constraints 2,208 20,800 5,048.00 2,208.00 232,208 MAX VALUE 379.18 4,728.30 0.94 1.23

Variables per cluster 93 704 194.96 93.00 8,968 MAX VALUE 231.83 160.17 0.82 1.23

Separator constraints 0 13,248 3,920.00 2,116.00 180,320 0 None 2,855.64 0.73 1.26

Separator variables 0 576 170.44 92.00 7,840 0 None 124.16 0.73 1.26

Clusters per variable 1 10 7.95 8.00 8,968 MAX VALUE 2,273.69 2.03 0.26 1.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2,208	20,800	5,048.00	2,208.00	232,208	MAX VALUE	379.18	4,728.30	0.94	1.23
Variables per cluster	93	704	194.96	93.00	8,968	MAX VALUE	231.83	160.17	0.82	1.23
Separator constraints	0	13,248	3,920.00	2,116.00	180,320	0	None	2,855.64	0.73	1.26
Separator variables	0	576	170.44	92.00	7,840	0	None	124.16	0.73	1.26
Clusters per variable	1	10	7.95	8.00	8,968	MAX VALUE	2,273.69	2.03	0.26	1.70

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 17,296
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-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 48.00 1.00 0.00 0.00 0.00 0.00

Degree 47 47 47.00 47.00 2,256 MAX VALUE 184.81 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 48 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	48.00	1.00	0.00	0.00	0.00	0.00
Degree	47	47	47.00	47.00	2,256	MAX VALUE	184.81	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	48	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: 17,296

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

Clustering coefficient 1.00 1.00 1.00 1.00 48.00 1.00 0.00 0.00 0.00 0.00

Degree 47 47 47.00 47.00 2,256 MAX VALUE 184.81 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 48 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	48.00	1.00	0.00	0.00	0.00	0.00
Degree	47	47	47.00	47.00	2,256	MAX VALUE	184.81	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	48	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: 8.16%
MCB compute time (ms): 112,250
MCB cycles: 50,761
Triangles: 795,616
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 570.20 0.00 -769.54 0.00 0.00 0.00

Degree 92 92 92.00 92.00 103,776 MAX VALUE 5,100.58 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 2,256 MAX VALUE 781.87 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 152,283 MAX VALUE 55,766.70 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	570.20	0.00	-769.54
Degree	92	92	92.00	92.00	103,776	MAX VALUE	5,100.58
Eccentricity	2	2	2.00	2.00	2,256	MAX VALUE	781.87
MCB cycle size	3	3	3.00	3.00	152,283	MAX VALUE	55,766.70

Minimal dual graph

Density: 0.35%
MCB compute time (ms): 23,131
MCB cycles: 1,086

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 20.13 0.02

Degree 2 7 3.91 4.00 4,416 MAX VALUE 1,506.65 0.97 0.25 1.26

Eccentricity 11 18 13.97 14.00 15,763 MAX VALUE 2,968.73 1.45 0.10 1.77

MCB cycle size 3 17 6.06 6.00 6,578 MAX VALUE 1,932.23 1.24 0.20 1.42

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	20.13	0.02
Degree	2	7	3.91	4.00	4,416	MAX VALUE	1,506.65	0.97	0.25	1.26
Eccentricity	11	18	13.97	14.00	15,763	MAX VALUE	2,968.73	1.45	0.10	1.77
MCB cycle size	3	17	6.06	6.00	6,578	MAX VALUE	1,932.23	1.24	0.20	1.42

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: 6.00%

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

Clustering coefficient 0.47 1.00 0.82 0.79 926.06 0.00 -240.69 0.15 0.18 4.20

Degree 2 304 67.57 9.00 76,216 MAX VALUE 3,213.46 100.59 1.49 3.87

Eccentricity 3 6 4.59 5.00 5,172 MAX VALUE 1,708.17 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	0.79	926.06	0.00	-240.69	0.15	0.18	4.20
Degree	2	304	67.57	9.00	76,216	MAX VALUE	3,213.46	100.59	1.49	3.87
Eccentricity	3	6	4.59	5.00	5,172	MAX VALUE	1,708.17	0.59	0.13	0.88

Incidence graph

Density: 0.33%
MCB compute time (ms): 2,062
MCB cycles: 1,081
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-16-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 47 3.84 2.00 4,512 MAX VALUE 966.68 8.90 2.32 0.17

Eccentricity 3 4 3.96 4.00 4,656 MAX VALUE 1,616.47 0.20 0.05 0.17

MCB cycle size 6 6 6.00 6.00 6,486 MAX VALUE 1,936.89 0.00 0.00 0.00

XCSP 2.1 Benchmarks