XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-13-ext
Number of variables: 39
Number of constraints: 741
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 39
Number of constraints: 741

General features

Coarse blocks: 57,382
Value tables: 39

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

Arity 2 2 2.00 2.00 1,482 MAX VALUE 513.62 0.00 0.00 0.00

Coarse blocks size 1 38 36.96 38.00 2,120,870 MAX VALUE 202,868.00 6.11 0.17 0.13

Relational linkage 0.03 0.03 0.03 0.03 28.33 0.00 -4,048.24 0.00 0.00 0.00

Tightness 0.03 0.98 0.06 0.03 43.80 0.00 -2,619.98 0.18 2.97 0.24

Tuples 25 1,482 1,431.09 1,482.00 1,060,440 MAX VALUE 5,309.41 266.99 0.19 0.24

Values 39 39 39.00 39.00 1,521 MAX VALUE 142.88 0.00 0.00 0.00

Value table constraints 38 38 38.00 38.00 1,482 MAX VALUE 141.87 0.00 0.00 0.00

Value table partitions 39 39 39.00 39.00 1,521 MAX VALUE 142.88 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	1,482	MAX VALUE	513.62	0.00	0.00	0.00
Coarse blocks size	1	38	36.96	38.00	2,120,870	MAX VALUE	202,868.00	6.11	0.17	0.13
Relational linkage	0.03	0.03	0.03	0.03	28.33	0.00	-4,048.24	0.00	0.00	0.00
Tightness	0.03	0.98	0.06	0.03	43.80	0.00	-2,619.98	0.18	2.97	0.24
Tuples	25	1,482	1,431.09	1,482.00	1,060,440	MAX VALUE	5,309.41	266.99	0.19	0.24
Values	39	39	39.00	39.00	1,521	MAX VALUE	142.88	0.00	0.00	0.00
Value table constraints	38	38	38.00	38.00	1,482	MAX VALUE	141.87	0.00	0.00	0.00
Value table partitions	39	39	39.00	39.00	1,521	MAX VALUE	142.88	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-3-13-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Tree1.json

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

Cluster constraints 741 741 741.00 741.00 741 741 6.61 0.00 0.00 0.00

Variables per cluster 39 39 39.00 39.00 39 39 3.66 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 39 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	741	741	741.00	741.00	741	741	6.61	0.00
Variables per cluster	39	39	39.00	39.00	39	39	3.66	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	39	1	0.00	0.00

Dual tree decomposition

Number of clusters: 37
Number of leaves: 19
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/DualTree1.json

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

Cluster constraints 1,443 11,908 3,100.00 1,443.00 114,700 MAX VALUE 288.40 2,621.16 0.85 1.41

Variables per cluster 75 488 147.54 75.00 5,459 MAX VALUE 177.52 108.11 0.73 1.41

Separator constraints 0 6,808 2,359.00 1,369.00 87,283 0 None 1,525.90 0.65 1.41

Separator variables 0 368 127.51 74.00 4,718 0 None 82.48 0.65 1.41

Clusters per variable 1 9 7.37 8.00 5,459 MAX VALUE 1,434.72 1.91 0.26 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,443	11,908	3,100.00	1,443.00	114,700	MAX VALUE	288.40	2,621.16	0.85	1.41
Variables per cluster	75	488	147.54	75.00	5,459	MAX VALUE	177.52	108.11	0.73	1.41
Separator constraints	0	6,808	2,359.00	1,369.00	87,283	0	None	1,525.90	0.65	1.41
Separator variables	0	368	127.51	74.00	4,718	0	None	82.48	0.65	1.41
Clusters per variable	1	9	7.37	8.00	5,459	MAX VALUE	1,434.72	1.91	0.26	1.58

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 9,139
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-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 39.00 1.00 0.00 0.00 0.00 0.00

Degree 38 38 38.00 38.00 1,482 MAX VALUE 141.87 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 39 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	39.00	1.00	0.00	0.00	0.00	0.00
Degree	38	38	38.00	38.00	1,482	MAX VALUE	141.87	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	39	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: 9,139

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

Clustering coefficient 1.00 1.00 1.00 1.00 39.00 1.00 0.00 0.00 0.00 0.00

Degree 38 38 38.00 38.00 1,482 MAX VALUE 141.87 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 39 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	39.00	1.00	0.00	0.00	0.00	0.00
Degree	38	38	38.00	38.00	1,482	MAX VALUE	141.87	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	39	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: 10.00%
MCB compute time (ms): 36,606
MCB cycles: 26,677
Triangles: 338,143
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 375.57 0.00 -503.54 0.00 0.00 0.00

Degree 74 74 74.00 74.00 54,834 MAX VALUE 3,189.31 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 1,482 MAX VALUE 513.62 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 80,031 MAX VALUE 29,307.70 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	375.57	0.00	-503.54
Degree	74	74	74.00	74.00	54,834	MAX VALUE	3,189.31
Eccentricity	2	2	2.00	2.00	1,482	MAX VALUE	513.62
MCB cycle size	3	3	3.00	3.00	80,031	MAX VALUE	29,307.70

Minimal dual graph

Density: 0.53%
MCB compute time (ms): 5,556
MCB cycles: 703

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 16.30 0.03

Degree 2 7 3.89 4.00 2,886 MAX VALUE 986.32 0.96 0.25 1.26

Eccentricity 9 15 12.13 12.00 8,987 MAX VALUE 1,845.37 1.23 0.10 1.61

MCB cycle size 3 15 5.97 6.00 4,195 MAX VALUE 1,240.54 1.22 0.20 1.43

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	16.30	0.03
Degree	2	7	3.89	4.00	2,886	MAX VALUE	986.32	0.96	0.25	1.26
Eccentricity	9	15	12.13	12.00	8,987	MAX VALUE	1,845.37	1.23	0.10	1.61
MCB cycle size	3	15	5.97	6.00	4,195	MAX VALUE	1,240.54	1.22	0.20	1.43

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: 6.66%

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

Clustering coefficient 0.47 1.00 0.81 0.77 601.98 0.00 -166.81 0.15 0.19 4.03

Degree 2 204 49.27 9.00 36,506 MAX VALUE 2,034.76 68.41 1.39 3.74

Eccentricity 3 5 4.20 4.00 3,114 MAX VALUE 1,055.68 0.61 0.15 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.77	601.98	0.00	-166.81	0.15	0.19	4.03
Degree	2	204	49.27	9.00	36,506	MAX VALUE	2,034.76	68.41	1.39	3.74
Eccentricity	3	5	4.20	4.00	3,114	MAX VALUE	1,055.68	0.61	0.15	0.91

Incidence graph

Density: 0.49%
MCB compute time (ms): 793
MCB cycles: 703
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-13-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 38 3.80 2.00 2,964 MAX VALUE 655.49 7.85 2.06 0.20

Eccentricity 3 4 3.95 4.00 3,081 MAX VALUE 1,070.09 0.22 0.06 0.20

MCB cycle size 6 6 6.00 6.00 4,218 MAX VALUE 1,259.61 0.00 0.00 0.00

XCSP 2.1 Benchmarks