XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-10-ext
Number of variables: 30
Number of constraints: 435
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 30
Number of constraints: 435

General features

Coarse blocks: 25,840
Value tables: 30

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

Arity 2 2 2.00 2.00 870 MAX VALUE 301.52 0.00 0.00 0.00

Coarse blocks size 1 29 27.98 29.00 723,040 MAX VALUE 83,845.70 5.24 0.19 0.16

Relational linkage 0.03 0.03 0.03 0.03 21.33 0.00 -2,176.77 0.00 0.00 0.00

Tightness 0.03 0.98 0.08 0.03 33.31 0.00 -1,412.03 0.20 2.57 0.29

Tuples 19 870 831.08 870.00 361,520 MAX VALUE 2,871.91 177.29 0.21 0.29

Values 30 30 30.00 30.00 900 MAX VALUE 102.04 0.00 0.00 0.00

Value table constraints 29 29 29.00 29.00 870 MAX VALUE 101.02 0.00 0.00 0.00

Value table partitions 30 30 30.00 30.00 900 MAX VALUE 102.04 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	870	MAX VALUE	301.52	0.00	0.00	0.00
Coarse blocks size	1	29	27.98	29.00	723,040	MAX VALUE	83,845.70	5.24	0.19	0.16
Relational linkage	0.03	0.03	0.03	0.03	21.33	0.00	-2,176.77	0.00	0.00	0.00
Tightness	0.03	0.98	0.08	0.03	33.31	0.00	-1,412.03	0.20	2.57	0.29
Tuples	19	870	831.08	870.00	361,520	MAX VALUE	2,871.91	177.29	0.21	0.29
Values	30	30	30.00	30.00	900	MAX VALUE	102.04	0.00	0.00	0.00
Value table constraints	29	29	29.00	29.00	870	MAX VALUE	101.02	0.00	0.00	0.00
Value table partitions	30	30	30.00	30.00	900	MAX VALUE	102.04	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-3-10-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Tree1.json

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

Cluster constraints 435 435 435.00 435.00 435 435 6.08 0.00 0.00 0.00

Variables per cluster 30 30 30.00 30.00 30 30 3.40 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 30 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	435	435	435.00	435.00	435	435	6.08	0.00
Variables per cluster	30	30	30.00	30.00	30	30	3.40	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	30	1	0.00	0.00

Dual tree decomposition

Number of clusters: 28
Number of leaves: 15
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/DualTree1.json

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

Cluster constraints 840 5,376 1,667.00 840.00 46,676 MAX VALUE 202.05 1,233.73 0.74 1.28

Variables per cluster 57 288 103.54 57.00 2,899 MAX VALUE 125.49 65.70 0.63 1.28

Separator constraints 0 3,136 1,232.00 784.00 34,496 0 None 698.80 0.57 1.28

Separator variables 0 224 88.00 56.00 2,464 0 None 49.91 0.57 1.28

Clusters per variable 1 8 6.66 7.00 2,899 MAX VALUE 796.10 1.80 0.27 1.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	840	5,376	1,667.00	840.00	46,676	MAX VALUE	202.05	1,233.73	0.74	1.28
Variables per cluster	57	288	103.54	57.00	2,899	MAX VALUE	125.49	65.70	0.63	1.28
Separator constraints	0	3,136	1,232.00	784.00	34,496	0	None	698.80	0.57	1.28
Separator variables	0	224	88.00	56.00	2,464	0	None	49.91	0.57	1.28
Clusters per variable	1	8	6.66	7.00	2,899	MAX VALUE	796.10	1.80	0.27	1.45

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 4,060
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-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 30.00 1.00 0.00 0.00 0.00 0.00

Degree 29 29 29.00 29.00 870 MAX VALUE 101.02 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 30 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	30.00	1.00	0.00	0.00	0.00	0.00
Degree	29	29	29.00	29.00	870	MAX VALUE	101.02	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	30	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: 4,060

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

Clustering coefficient 1.00 1.00 1.00 1.00 30.00 1.00 0.00 0.00 0.00 0.00

Degree 29 29 29.00 29.00 870 MAX VALUE 101.02 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 30 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	30.00	1.00	0.00	0.00	0.00	0.00
Degree	29	29	29.00	29.00	870	MAX VALUE	101.02	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	30	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: 12.90%
MCB compute time (ms): 8,051
MCB cycles: 11,746
Triangles: 113,680
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 221.46 0.00 -293.68 0.00 0.00 0.00

Degree 56 56 56.00 56.00 24,360 MAX VALUE 1,751.03 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 870 MAX VALUE 301.52 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 35,238 MAX VALUE 12,904.30 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	221.46	0.00	-293.68
Degree	56	56	56.00	56.00	24,360	MAX VALUE	1,751.03
Eccentricity	2	2	2.00	2.00	870	MAX VALUE	301.52
MCB cycle size	3	3	3.00	3.00	35,238	MAX VALUE	12,904.30

Minimal dual graph

Density: 0.89%
MCB compute time (ms): 1,439
MCB cycles: 408

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 0.02 12.47 0.05

Degree 2 7 3.86 4.00 1,680 MAX VALUE 575.72 0.93 0.24 1.24

Eccentricity 8 13 10.39 10.00 4,519 MAX VALUE 1,016.36 0.95 0.09 1.36

MCB cycle size 3 14 5.86 6.00 2,390 MAX VALUE 712.52 1.21 0.21 1.47

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	0.02	12.47	0.05
Degree	2	7	3.86	4.00	1,680	MAX VALUE	575.72	0.93	0.24	1.24
Eccentricity	8	13	10.39	10.00	4,519	MAX VALUE	1,016.36	0.95	0.09	1.36
MCB cycle size	3	14	5.86	6.00	2,390	MAX VALUE	712.52	1.21	0.21	1.47

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: 8.59%

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

Clustering coefficient 0.47 1.00 0.81 0.76 353.04 0.00 -98.45 0.15 0.19 3.79

Degree 2 136 37.26 9.00 16,210 MAX VALUE 1,151.67 47.41 1.27 3.50

Eccentricity 3 5 3.87 4.00 1,682 MAX VALUE 583.45 0.57 0.15 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.76	353.04	0.00	-98.45	0.15	0.19	3.79
Degree	2	136	37.26	9.00	16,210	MAX VALUE	1,151.67	47.41	1.27	3.50
Eccentricity	3	5	3.87	4.00	1,682	MAX VALUE	583.45	0.57	0.15	0.85

Incidence graph

Density: 0.81%
MCB compute time (ms): 257
MCB cycles: 406
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-10-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 29 3.74 2.00 1,740 MAX VALUE 402.54 6.63 1.77 0.24

Eccentricity 3 4 3.94 4.00 1,830 MAX VALUE 636.00 0.25 0.06 0.24

MCB cycle size 6 6 6.00 6.00 2,436 MAX VALUE 727.45 0.00 0.00 0.00

XCSP 2.1 Benchmarks