XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-7-ext
Number of variables: 21
Number of constraints: 210
Satisfiable: True
Timestamp: 2025-07-20 22:08:33
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 21
Number of constraints: 210

General features

Coarse blocks: 8,680
Value tables: 21

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

Arity 2 2 2.00 2.00 420 MAX VALUE 145.56 0.00 0.00 0.00

Coarse blocks size 1 20 19.02 20.00 165,088 MAX VALUE 24,660.90 4.20 0.22 0.20

Relational linkage 0.05 0.05 0.05 0.05 14.33 0.00 -916.40 0.00 0.00 0.00

Tightness 0.05 0.97 0.11 0.05 22.83 0.00 -597.24 0.23 2.10 0.37

Tuples 13 420 393.07 420.00 82,544 MAX VALUE 1,222.60 100.78 0.26 0.37

Values 21 21 21.00 21.00 441 5.84e+27 63.94 0.00 0.00 0.00

Value table constraints 20 20 20.00 20.00 420 2.10e+27 62.91 0.00 0.00 0.00

Value table partitions 21 21 21.00 21.00 441 5.84e+27 63.94 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	420	MAX VALUE	145.56	0.00	0.00	0.00
Coarse blocks size	1	20	19.02	20.00	165,088	MAX VALUE	24,660.90	4.20	0.22	0.20
Relational linkage	0.05	0.05	0.05	0.05	14.33	0.00	-916.40	0.00	0.00	0.00
Tightness	0.05	0.97	0.11	0.05	22.83	0.00	-597.24	0.23	2.10	0.37
Tuples	13	420	393.07	420.00	82,544	MAX VALUE	1,222.60	100.78	0.26	0.37
Values	21	21	21.00	21.00	441	5.84e+27	63.94	0.00	0.00	0.00
Value table constraints	20	20	20.00	20.00	420	2.10e+27	62.91	0.00	0.00	0.00
Value table partitions	21	21	21.00	21.00	441	5.84e+27	63.94	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-3-7-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Tree1.json

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

Cluster constraints 210 210 210.00 210.00 210 210 5.35 0.00 0.00 0.00

Variables per cluster 21 21 21.00 21.00 21 21 3.04 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 21 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	210	210	210.00	210.00	210	210	5.35	0.00
Variables per cluster	21	21	21.00	21.00	21	21	3.04	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	21	1	0.00	0.00

Dual tree decomposition

Number of clusters: 19
Number of leaves: 10
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/DualTree1.json

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

Cluster constraints 399 1,848 707.00 399.00 13,433 MAX VALUE 121.88 427.03 0.60 1.37

Variables per cluster 39 144 63.37 39.00 1,204 2.18e+33 76.77 32.22 0.51 1.37

Separator constraints 0 988 497.00 361.00 9,443 0 None 237.57 0.48 1.37

Separator variables 0 104 52.32 38.00 994 0 None 25.01 0.48 1.37

Clusters per variable 1 7 5.73 6.00 1,204 MAX VALUE 351.02 1.65 0.29 1.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	399	1,848	707.00	399.00	13,433	MAX VALUE	121.88	427.03	0.60	1.37
Variables per cluster	39	144	63.37	39.00	1,204	2.18e+33	76.77	32.22	0.51	1.37
Separator constraints	0	988	497.00	361.00	9,443	0	None	237.57	0.48	1.37
Separator variables	0	104	52.32	38.00	994	0	None	25.01	0.48	1.37
Clusters per variable	1	7	5.73	6.00	1,204	MAX VALUE	351.02	1.65	0.29	1.46

Primal graph

Density: 100.00%
MCB compute time (ms): 2
MCB cycles: 190
Triangles: 1,330
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-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 21.00 1.00 0.00 0.00 0.00 0.00

Degree 20 20 20.00 20.00 420 2.10e+27 62.91 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 570 MAX VALUE 208.74 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	21.00	1.00	0.00	0.00	0.00	0.00
Degree	20	20	20.00	20.00	420	2.10e+27	62.91	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	570	MAX VALUE	208.74	0.00	0.00	0.00

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): 2
MCB cycles: 190
Triangles: 1,330

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

Clustering coefficient 1.00 1.00 1.00 1.00 21.00 1.00 0.00 0.00 0.00 0.00

Degree 20 20 20.00 20.00 420 2.10e+27 62.91 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 570 MAX VALUE 208.74 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	21.00	1.00	0.00	0.00	0.00	0.00
Degree	20	20	20.00	20.00	420	2.10e+27	62.91	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	570	MAX VALUE	208.74	0.00	0.00	0.00

Dual graph

Density: 18.18%
MCB compute time (ms): 338
MCB cycles: 3,781
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 107.84 0.00 -139.96 0.00 0.00 0.00

Degree 38 38 38.00 38.00 7,980 MAX VALUE 763.89 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 11,343 MAX VALUE 4,153.85 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	0.51	0.51	0.51	107.84	0.00	-139.96	0.00	0.00	0.00
Degree	38	38	38.00	38.00	7,980	MAX VALUE	763.89	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	11,343	MAX VALUE	4,153.85	0.00	0.00	0.00

Minimal dual graph

Density: 1.82%
MCB compute time (ms): 101
MCB cycles: 190

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 8.64 0.08

Degree 2 6 3.80 4.00 798 MAX VALUE 274.80 0.89 0.24 1.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 11 5.75 6.00 1,093 MAX VALUE 328.72 1.13 0.20 1.44

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	8.64	0.08
Degree	2	6	3.80	4.00	798	MAX VALUE	274.80	0.89	0.24	1.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	11	5.75	6.00	1,093	MAX VALUE	328.72	1.13	0.20	1.44

Triangulated dual graph

Density: 72.73%
Triangles: 753,038

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

Clustering coefficient 0.84 1.00 0.89 0.87 186.48 0.00 -25.26 0.05 0.06 1.92

Degree 38 185 152.00 172.00 31,920 MAX VALUE 1,041.40 43.15 0.28 1.92

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	0.84	1.00	0.89	0.87	186.48	0.00	-25.26	0.05	0.06	1.92
Degree	38	185	152.00	172.00	31,920	MAX VALUE	1,041.40	43.15	0.28	1.92
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.23%

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

Clustering coefficient 0.47 1.00 0.79 0.75 166.32 0.00 -53.35 0.16 0.20 3.53

Degree 2 75 23.47 9.00 4,928 MAX VALUE 519.90 25.19 1.07 3.25

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	0.47	1.00	0.79	0.75	166.32	0.00	-53.35	0.16	0.20	3.53
Degree	2	75	23.47	9.00	4,928	MAX VALUE	519.90	25.19	1.07	3.25
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.58%
MCB compute time (ms): 22
MCB cycles: 190
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-7-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 20 3.64 2.00 840 MAX VALUE 208.47 5.17 1.42 0.30

Eccentricity None None None None None None None None None None

MCB cycle size 6 6 6.00 6.00 1,140 MAX VALUE 340.43 0.00 0.00 0.00

XCSP 2.1 Benchmarks